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Product Description Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 3rd Edition Algebra 2 textbook and tests/worksheets book & answer key, as well as the DIVE Algebra 2 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Algebra 2 covers geometric functions like angles, perimeters, and proportional segments; negative exponents; quadratic equations; metric conversions; logarithms; and advanced factoring. The DIVE software teaches Saxon lesson concepts step-by-step on a digital whiteboard, each lesson averaging about 10-15 minutes in length. Because guide. Product Reviews Saxon Algebra 2 Kit & DIVE CD-Rom, Third Edition 5 5 1 1 Saxon Algebra 2 w/ DIVE CD I've used ALL the Saxon Math books along with the DIVE CD starting in the 78 series. I've been completely satisfied with the Saxon and DIVE lessons. After finishing the Algebra II lessons, I was surprised to discover the Saxon books did not cover ALL the Algebra concepts (85%). Luckily, with the help of the DIVE CD series for Algebra II, my son was able to complete the needed Algebra to qualify to pass his CLEP exams. I'm not familiar with the Saxon CD series, but we did review a sample Saxon CD and my son found he liked the DIVE better, which I enjoyed because it's cheaper then the Saxon, plus my son seemed to relate better DIVE. I gave a four star rating for "Meets Expectation" due to the number of errors and typo's I found in this book. But luckily you can find them on the Saxon Home page. I just didn't like having to track them down. I have enough to do as a home-school mom. But I love Saxon Math and will never sell or give away my library of them. They can always be used for future grandkids too. October 30, 2010
MathXL If you assessed into Math 50 (Mind Over Math), here is an independent study opportunity to practice your arithmetic skills for Math 51 (Pre-Algebra) or higher classes. Completing 5 modules in Math XL will prepare and allow you to retake the Mt. San Jacinto College Math Assessment test. The modules are Multiplication & Division of Fractions, Adding & Subtracting Fractions, Decimals, Percents, and Order of Operations. This is not a class, so there is no instructor. However, this independent study program will help you learn the concepts needed for Math 51. You will have access to exercises, videos, and practice quizzes. If you assessed into Math 050 and you are interested in getting started, select the MathXL picture below:
More About This Textbook Overview Algebra in the Elementary Classroom provides the support we need as teachers to embed the development of students' algebraic thinking in the teaching of elementary school. - Megan Loef Franke Coauthor of Children's Mathematics and Thinking Mathematically How do you start students down the road to mathematical understanding? By laying the foundation for algebra in the elementary grades. Algebra and the Elementary Classroom shares ideas, tasks, and practices for integrating algebraic thinking into your teaching. Through research-based and classroom-tested strategies, it demonstrates how to use materials you have on hand to prepare students for formal algebra instruction - without adding to your overstuffed curriculum. You'll find ways to: introduce algebraic thinking through familiar arithmetical contexts nurture it by helping students think about, represent, and build arguments for their mathematical ideas develop it by exploring mathematical structures and functional relationships strengthen it by asking students to make algebraic connections across the curriculum reinforce it across the grades through a schoolwide initiative. No matter what your math background is, Algebra and the Elementary Classroom offers strong support for integrating algebraic thinking into your daily teaching. Its clear descriptions show you what algebraic thinking is and how to teach it. Its sample problems deepen your own algebraic thinking. Best of all, it gives you ideas for grade-specific instructional planning. Read Algebra and the Elementary Classroom and prepare your students for a lifetime of mathematical understanding. Related Subjects Meet the Author Maria Blanton is the author of the Heinemann title Algebra and the Elementary Classroom (2008). She is Senior Executive Research Associate at the James J. Kaput Center for Research and Innovation in Mathematics Education and Associate Professor in the Department of Mathematics at the University of Massachusetts Dartmouth. Her work focuses on understanding issues of teacher and student learning associated with algebraic thinking in the elementary grades
Synopses & Reviews Publisher Comments: Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations. This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading
Graphing Functions In this tutorial, the viewer will learn about graphing functions. By working through the materials step-by-step and using sample questions for each section, you will be able to better understand this level of algebra. NOTE: This is part of a much lar...ger seven-hour clip on the topic. (35:29
More About This Textbook Overview In a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applications continues to be a best-seller because it shows students how we use mathematics in our daily lives and whythis is important. The Ninth Edition further emphasizes this with the addition of new "Why This Is Important" sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and a Product Details Meet the Author, more than fifteen years at State College of Florida–Manatee-Sarasota and for almost ten years
All professional education content courses leading to certification shall include teaching and assessment ofthe Wisconsin Content Standards in the content area. In this column, list the Wisconsin Content Standards that are included in this course. The Standards for each content area are found in the Wisconsin Content Standards document. In this column, indicate the nature of the performance assessments used in this course to evaluate student proficiency in each standard. The structures within the discipline, the historical roots and evolving nature of mathematics, and the interaction between technology and the discipline. Students study a selected topic under the direction of a faculty member. They normally work problems related to the material. These problems, depending on the topic studied, will usually assess at least one of structures, history, the evolution of mathematics or the use of technology. Facilitating the building of student conceptual and procedural understanding. The problems students work on are selected to insure the student understands the selected topic. Helping all students build understanding of the discipline including: . Confidence in their abilities to utilize mathematical knowledge. . Awareness of the usefulness of mathematics. . The economic implications of fine mathematical preparation. Studying the selected topic on their own and working problems related to that topic measure the student's ability to study and understand mathematics on their own with general guidance from an instructor. This measures both their confidence in using mathematics independently and awareness of how useful mathematics is. Exploring, conjecturing, examining and testing all aspects of problem solving. In many cases the selected topic involves a consideration of all aspects of solving a certain type of problem. The problems the student works out and submits will measure this. Often the student will need to formulate the appropriate mathematical questions as part of the work they submit, constructing either a counter-example or a proof for their conjectures. Expressing ideas orally, in writing, and visually-, using mathematical language, notation, and symbolism; translating mathematical ideas between and among contexts. Students will typically give an oral report on their progress on a regular basis to the faculty member directing their work. Worked problems will in most cases include mathematical notation and language. Connecting the concepts and procedures of mathematics, drawing connections between mathematical strands, between mathematics and other disciplines, and with daily life. Depending on the topic studied, problems connecting mathematical concepts, other disciplines and daily life are done. Selecting appropriate representations to facilitate mathematical problem solving and translating between and among representations to explicate problem-solving situations. For selected topics of study students may work problems that involve selecting the appropriate representation. Mathematical processes including: . Problem solving. . Communication. . Reasoning and formal and informal argument. . Mathematical connections. . Representations. . Technology. Depending on the subject selected, submitted problems can involve any one or a combination of these six mathematical processes. Number operations and relationships from both abstract and concrete perspectives identifying real world applications, and representing and connecting mathematical concepts and procedures including: . Number sense. . Set theory. . Number and operation. . Composition and decomposition of numbers, including place value, primes, factors, multiples, inverses, and the extension of these concepts throughout mathematics. . Number systems through the real numbers, their properties and relations. . Computational procedures. . Proportional reasoning. . Number theory. Depending on the topic studied, problems on these topics could be done. Mathematical concepts and procedures, and the connections among them for teaching upper level number operations and relationships including: . Advanced counting procedures, including union and intersection of sets, and parenthetical operations. . Algebraic and transcendental numbers. . The complex number system, including polar coordinates. . Approximation techniques as a basis for numerical integration, fractals, and numerical-based proofs. . Situations in which numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social) can be created and critically evaluated. . Opportunities in which acceptable limits of error can be assessed (e.g., evaluating strategies, testing the reasonableness of results, and using technology to carry out computations). Depending on the topic studied, problems on these topics could be done. If the topic selected involved teaching number operations and relationships, a presentation or paper on these subject areas would be done. Geometry and measurement from both abstract and concrete perspectives and to identify real world applications, and mathematical concepts, procedures and connections among them including: . Formal and informal argument. . Names, properties, and relationships of two- and three-dimensional shapes. . Spatial sense. . Spatial reasoning and the use of geometric models to represent, visualize, and solve problems. . Transformations and the ways in which rotation, reflection, and translation of shapes can illustrate concepts, properties, and relationships. . Coordinate geometry systems including relations between coordinate and synthetic geometry, and generalizing geometric principles from a two-dimensional system to a three-dimensional system. . Concepts of measurement, including measurable attributes, standard and non-standard units, precision and accuracy, and use of appropriate tools. . The structure of systems of measurement, including the development and use of measurement systems and the relationships among different systems. Measurement including length, area, volume, size of angles, weight and mass, time, temperature, and money. . Measuring, estimating, and using measurement to describe and compare geometric phenomena. . Indirect measurement and its uses, including developing formulas and procedures for determining measure to solve problems. If a geometry topic is selected for study students would typically work problems from one or more of these areas. Mathematical concepts, procedures, and the connections among them for teaching upper level geometry and measurement including: . Transformations, coordinates, and vectors and their use in problem solving. Three-dimensional geometry and its generalization to other dimensions. Topology, including topological properties and transformations. . Opportunities to present convincing arguments by means of demonstration, informal proof, counter-examples, or other logical means to show the truth of statements and/or generalizations. If teaching geometry is selected for study students would give a presentation or a paper on work done in these areas. Statistics and probability from both abstract and concrete perspectives and to identify real world applications, and the mathematical concepts, procedures and the connections between them including: . Use of data to explore real-world issues. . The process of investigation including formulation of a problem, designing a data collection plan, and collecting, recording, and organizing data. . Probability as a way to describe chances or risk in simple and compound events. . Outcome prediction based on experimentation or theoretical probabilities. Problems from one or more of these areas would often be done if statistics or probability is selected as the subject studied. Mathematical concepts, procedures, and the connections among them for teaching upper level statistics and probability including: . Use of the random variable in the generation and interpretation of probability distributions. . Descriptive and inferential statistics, measures of disbursement, including validity and reliability, and correlation. . Probability theory and its link to inferential statistics. . Discrete and continuous probability distributions as bases for inference. . Situations in which students can analyze, evaluate, and critique the methods and conclusions of statistical experiments reported in journals, magazines, news media, advertising, etc. If teaching statistics or probability is the subject selected for study, a paper or a presentation on what was covered related to these area would be done. Functions, algebra, and basic concepts underlying calculus from both abstract and concrete perspectives and to identify real world applications, and the mathematical concepts, procedures and the connections among them including: . Patterns. . Functions as used to describe relations and to model real world situations. . Representations of situations that involve variable quantities with expressions, equations and inequalities and that include algebraic and geometric relationships. . Multiple representations of relations, the strengths and limitations of each representation, and conversion from one representation to another.
The widespread use of computers and the rapid growth in computer science have led to a new emphasis on discrete mathematics, a discipline which deals with calculations involving a finite number of steps. This book provides a well-structured introduction to discrete mathematics, taking a self-contained approach that requires no ancillary knowledge of mathematics, avoids unnecessary abstraction, and incorporates a wide rage of topics, including graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra. Amply illustrated with examples and exercises. Numbers And Counting Integers Functions and counting Principles of counting Subsets and designs Partition, classification, and distribution Modular arithmetic Graphs And Algorithms Algorithms and their efficiency Graphs Trees, sorting, and searching Bipartite graphs and matching problems Digraphs, networks, and flows Recursive techniques Algebraic Methods Groups Groups of permutations Rings, fields, and polynomials Finite fields and some applications Error-correcting codes Generating functions Partitions of a positive integer Symmetry and counting
Vector Calculus Book summary This book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. The organization of the text draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in its approach, it is written with an assumption that the reader may have computing facilities for two- and three-dimensional graphics and for doing symbolic algebra. The book contains many figures, and encourages the reader to viszualize with the aid of hand drawings and computers, and through expositions and exercises. It introduces geometry in three-dimensional space, together with Cylindrical and Spherical Co-ordinates, anticipating their later use in connection with the Chain Rule and change of variable in double and triple integrals. It also introduces matrix notation and the rudiments of linear algebra to facilitate exposition. It also provides approximately 1200 exercises, including drills, applications, proofs and "technologically active" projects. [via]
Function Function (Encyclopedia of Science) A function is a mathematical relationship between two sets of real numbers. These sets of numbers are related to each other by a rule that assigns each value from one set to exactly one value in the other set. For example, suppose we choose the letter x to stand for the numbers in one set and the letter y for the numbers in the second set. Then, for each value we assign to x, we can find one and only one comparable value of y. An example of a function is the mathematical equation y = 3x + 2. For any given value of x, there is one and only one value of y. If we choose 5 for the value of x, then y must be equal to 17 (3 · 5 + 2 = 17). Or if we choose 11 for the value of x, then y must be equal to 35 (3 · 11 + 2 = 35). The standard notation for a function is y = f(x) and is read "y equals f of x." Functions can also be represented in other ways, such as by graphs and tables. Functions are classified by the types of rules that govern their relationships: algebraic, trigonometric, logarithmic, and exponential. Mathematicians and scientists have found that elementary functions represent many real-world phenomena. Characteristics of functions The idea of a function is very important in mathematics because it describes any situation in which one quantity depends on another. For example, the height of a person depends, to a... (The entire section is 960
After costs so that your next education can be free once you have right devices to read these like ipad, netbooks, laptops and desktops. We are so happy that these clustered contents are making changes in the under served continents but having Internet connectivity. The Book on Mathematics will give you a good insight of topics usually read by class 10th students. Below is the overview of book chapters. This is 45 chapter free pdf book and hard to find for general surfers. 4 Responses to Grade-10 Free Series: A Good Conceptual Mathematics pdf book This is such a great resource that you are providing and you give it away for free. I enjoy seeing websites that understand the value of providing a prime resource for free. I truly loved reading your post. Thanks!
IV.BEHAVIORAL OBJECTIVES The objectives and competencies proposed for this course will be demonstrated as students work with the following: Systems of Linear Equations. Gaussian Elimination. Homogeneous Systems of Linear Equations. Matrices and Matrix Operations. Inevitability. Determinant Function. Determinant by Row Reduction. Cramer's Rule. Vectors and Vector Operations in 2-Dimensional and 3-Dimensional Space. Norm of a Vector. Dot Product and Projections. Cross Product. Lines and Planes in 3-Dimensional Space. Euclidean N-Space. General Vector Spaces. Subspaces. Linear Independence. Basis and Dimension Row and Column Spaces of a Matrix, Rank. Linear Transformations Properties of Linear Transformations; Kernal and Range. Eigenvalues and Eigenvectors. Diagonalization. V.EVALUATION CRITERIA/GRADING SCALE There will be four tests and a comprehensive final exam. The grading scale for determining the course grade and the weights assigned to tests, final examination, and homework are given below. The in class tests and final exam will be graded on a 100 point scale. Homework will be collected randomly at a rate averaging about once a week and given a grade of either pass or fail. The homework score will depend on the percentage of passing grades assigned for collected assignments. Late homeworks will not be accepted and the final exam grade will be used as the grade for all tests that are missed. Make up tests will not be given. The lowest score for an in class test will be dropped and the class test average will be computed as in the example below. The percentage of passing homework grades will be multiplied by four, rounded, and the result added to the test average. Example: To see how your grade will be calculated, suppose your test scores are 81, 84, 75, and 90, your final exam score is 88 and you received a passing grade on 50% of the homework collected. Since the lowest test grade is dropped (see item 1 under COURSE REQUIREMENTS), your grade would be calculated as follows: 0.20 * [ (81 + 85 + 84 + 90) ] + 0.20 * 88 = 85.6 85.6 + .50*4 = 85.6 + 2 = 87.6 = 88 Since 88 is between 80 and 89 you would receive a grade of B. Weights Assigned to graded materials: In Class Tests 20% Each Comprehensive Final Examination 20% Homework 4% Extra Credit Grading Scale: A 92-100% Assignments 10% B 83-91% Tests 30% C 73-82% Final Exam 30% D 64-72% F Below 63% VI.READING ASSIGNMENTS: Read each section prior to the presentation of the topic in class. VII.COURSE REQUIREMENTS Conduct of Course/Classroom Decorum 1. Students are responsible for availing themselves of all class meetings and individual help from the instructor. 2. Students are responsible for maintaining a notebook of problems selected by the instructor. Students are encouraged to include as many additional problems as is possible 3. All tests will be announced prior to their administration. Since the lowest test will be dropped no make-up test will be given. There will be a test given at the end of each chapter, except possibly for chapter 6, and there will be a comprehensive final examination given. 4. Students are expected to enter the classroom on time and remain until the class ends. Late arrivals and early departures will be noted in the record book. The class attendance policy set forth in the 1996-1998 FSU Catalogue will be strictly adhered to. 5. Students must refrain from smoking, eating, and drinking in the classroom. The rights of others must be respected at all times. 6. Students are encouraged to ask questions of the instructor in class and to respond to those posed by the instructor. They should not discourage others from asking or answering questions. Other students often have the same questions on their minds, but are hesitant to ask. 7. Students are expected to complete all class assignments and to spend adequate time on their class work and to read each topic prior to class discussion to insure that the course objectives are met. Two hours of home study is expected for each hour of class. 8. Talking in class between students is strictly unacceptable. Discussions should be directed to the instructor. 9. Extra recitation periods and/or computer lab attendance are mandatory for students whose grades fall below C. They must meet the instructor to arrange for extra activities. 10. Dishonesty on graded assignments will not be tolerated. Students must neither give nor receive help on any work to be graded. The University policy on cheating will be applied to any violations. The minimum penalty will be a grade of zero on the assignment.
Office hours Sequences and Series will challenge us to think very carefully about "infinity." What does it mean to add up an unending list of numbers? How can an infinite task result in a finite answer? These questions lead us to some very deep concepts—but also to some powerful computational tools which are used not only in math but in many quantitative disciplines. This course is a first introduction to sequences, infinite series, convergence tests, and Taylor series. It is suitable for someone who has seen just a bit of calculus before. Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. This online course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.
Polynomial Equations over Matices. File(s): If we are given an n-th degree polynomial over the complex numbers, we know that it has exactly n solutions. However, this is not true for an n-th degree polynomial over matrices. The difference in the two cases is that multiplication of matices is not commutative (AB does not equal BA) and not all matrices are invertible. The question then becomes: how many solutions can exist? Description Color poster with text and equations. Sponsor(s) University of Wisconsin--Eau Claire Office of Research and Sponsored Programs.
Elementary And Intermediate will get more out of Elementary and Intermediate Algebra through George Woodbury's concise narrative and focused topic flow. By writing this text from the ground up as a single textbook, George has reduced the amount of overlap typically found in these courses and focused instead on providing more exercises and applications. As a result, your students will be better prepared for higher-level mathematics courses.
MATHChester Higgins Jr./The New York TimesRemedial math class for incoming freshmen at Borough of Manhattan Community College. When I sat through a remedial math class at the Borough of Manhattan Community College one recent morning, I was a bit surprised and more than a little embarrassed to realize that it was tough for me to follow along. Quadratic equations? Line slopes? Scientific notation? My mind was dizzy. Granted, I told myself, it had been more than a decade since I took a math class of any kind. And truth be told, I was no algebraic genius. But this was supposed to be remedial math. These are very basic concepts that the city is trying to ensure all of its high school graduates know. Apparently, I was not alone. This morning I received more than 30 e-mails from other folks who were stumped on the same problem that tripped up a recent city high school graduate. Turns out we all may have erased ninth grade from memory. So here we offer you a chance for more: the entire weekly worksheet given to students in Steven Mandelkorn's remedial math class at B.M.C.C. For starters try problem 10: A number is six more than the product of negative three and n. Read more…
In Algebra 1 the topic of Polynomials and Factoring is a very important in many aspects. .... lesson plan will utilize certain examples in order to get the students to think of the subject in depth. This lesson ... help students develop a full understanding of a lesson concept. ... An example of an instructional ... skills such as phonics or basic math facts to mastery. .... The 5E Instructional Model has its roots in the ideas of Johann Herbart, John Dewey, ... (Algebra–Based) .... In the latter part of the 18th century it was realized that any sample of matter has a ..... unit charge at the location of Q. This quantity (which is a vector, since force is a vector) ... which is a distance z from the plane; see Fig. in your algebra class, you need a plan. MAKE TIME FOR THE .... Here are some more examples of algebraic expressions. ..... physical activity that day from the calories he/she ingests that day. Translate ... Maximizing Algebra II Performance ... the data sets, participants will work in small groups to study a sample lesson plan that ... After analyzing the 5E lesson plan, participants will generate questions that ... This Concept Development Unit walks students through the algebraic process for solving ... each of the groups of four to demonstrate one of their examples on the board or ... solving equations while introducing the idea of representing ideas.
Math Club The representative body of mathematics students are committed to strengthening the math department and students' experiences in math. The Math Club is an outlet to promote mathematics across the campus and acts as a forum for addressing mathematics students' concerns.
Introduction to MATLAB Regístrese a este webinar rellenándo este formulario Join us online as we introduce MATLAB, a high-level language and interactive environment for numerical computation, visualization, and programming. MATLAB includes built-in mathematical functions fundamental to solving engineering and scientific problems, and an interactive environment ideal for iterative exploration, design, and problem solving. Through product demonstrations, you will see how this combination allows you to quickly explore ideas, gain insight into your data, and document and share your results. Please allow approximately 60 minutes to attend the presentation and Q&A session.
Interactive Tests - Ron Knott Ron Knott has begun producing Mathematics A and AS Level tests for the independent UK curriculum development body, Mathematics in Education and Industry. The web-based format of the tests let you view a problem and then: choose an answer from a multiple ...more>> InterMath - The University of Georgia InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. InterMath workshops provide an ongoing support community, a lesson plan database, and a discussion board. The site provides mathematical ...more>> International Mathematical Olympiad - John Webb Search or download problems from every year of the International Mathematical Olympiad (IMO), dating back to the first competition, in 1959. Problems from 2003-2005 may be downloaded in Spanish as well as English; and from 2006 forward, in dozens more ...more>> An Introduction to Continued Fractions - Ron Knott Continued fractions are just another way of writing fractions. They have some interesting links with a jigsaw-puzzle problem of splitting a rectangle up into squares and also with one of the oldest algorithms known to mathematicians - Euclid's Algorithm ...more>> Investigations in Mathematics - Eric S. Rowland Open-ended problems for high school and college students to "approach creatively and in their own way": Pascal's simplices ("What is the generalization of Pascal's triangle?"), Pythagorean triples, regular polygons ("What is the area of a regular polygon ...more>> IUP Annual Mathematics Competition - Gary Stoudt A mathematics competition for high school students sponsored by Indiana University of Pennsylvania. Topics include algebra, geometry, and trigonometry. Registration forms may be found online, and previous competitions may be downloaded in PDF, PostScript,JavaSketchpad DR3 Gallery - Key Curriculum Press JavaSketchpad is software that lets you publish sketches from The Geometer's Sketchpad on the Internet. If you have a Java-compatible Web browser, visit this demo gallery for some examples of JavaSketchpad in use: Centroid; Stereo Icosahedron; Hypercube; ...more>> Jefferson Math Project - Steve Sibol Resources for integrating Math A and Math B Regents exam questions into the New York State curriculum. PDF, Microsoft Word, and Worksheet Builder versions of exams date back to 1999. See also the JMAP worksheets of Regents questions coordinated with the ...more>> Jim Loy's Puzzle Page - Jim Loy This is a group of number, geometry, and logic puzzles with solutions, including "The Missing Dollar," "The Monty Hall Trap," and comments on the Tower of Hanoi. ...more>> János Bolyai Mathematical Society A Hungarian mathematical society. Conference information, books published by the society, and problems from the Schweitzer Miklós Mathematical Competition. More information is available in Hungarian. ...more>> John Conway's Game of Life - Stephen Stuart The Game of Life is played on a field of cells, each of which has eight neighbors (adjacent cells). A cell is either occupied (by an organism) or not. The rules for deriving a generation from the previous one are these: Death - If an occupied cell has ...more>> John Mason's Projects - John Mason Projects by the author of Thinking Mathematically and former director of the Centre for Mathematics Education: Structured Variation Grids and other animations and applets; studies in algebraic thinking; mathematical explorations; MEMEs (Meaning Enquiry ...more>> Joy of Problem Solving - Deepak Kulkarni Math olympiad programs for elementary and middle school kids by a Ph. D. in computer science and former NASA researcher. See, in particular, the section of Kulkarni's site entitled "How to Work on Problems," which includes essays such as Problem Solving ...more>>
Modeling the Dynamics of Life - 3rd edition Summary: Understand the role of mathematics in biology with MODELING THE DYNAMICS OF LIFE: CALCULUS AND PROBABILITY FOR LIFE SCIENTISTS, Third Edition! Designed to demonstrate the importance of mathematics in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, this mathematics text provides you with the tools you need to succeed. Modeling problems, review problems, and over 100 graphing calculator or computer exercises help you visualize and conceptual...show moreize
Summary: The authors help students ''see the math'' through their focus on functions;visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; andexamples and exercises. By remaining focused on today's students and their needs, the authorslead students to mathematical understandingand, ultimately,success in class
More About This Textbook Overview Exploring Numerical Methods is designed to provide beginning engineering and science students, as well as upper-level mathematics students, with an introduction to numerical analysis that emphasizes insight and hands-on experience. To serve the needs of both the younger and the more experienced audience, each chapter begins with an intuitive presentation of motivation and simple algorithms. Topics are developed progressively within each chapter and the advanced material, which reveals underlying theory and discusses complicated methods, is clearly marked. The text takes a focused approach to introducing the more important numerical algorithms and exposes students to partial differential equations by using simple prototypes. This text provides a strong experiential basis for future
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike. Readership Graduate students, mathematicians, and historians. Reviews "Provide[s] a broad and clear overview of the mathematics leading to, and growing out of, the work of Cartan. For anyone wishing to understand something of Cartan's mathematics and its historical context, this book will provide a good starting point and a continuing helpful reference work ... the authors have performed an invaluable service for anyone interested in what Cartan achieved and how it relates to subsequent developments."
Algebra for College Students - 5th edition ISBN13:978-0077224844 ISBN10: 0077224841 This edition has also been released as: ISBN13: 978-0073533520 ISBN10: 0073533521 Summary: Algebra for College Students, 5/e is part of the latest offerings in the successful Dugopolski series in mathematics. The authors goal is to explain mathematical concepts to students in a language they can understand. Dugopolski includes a double cross-referencing system between the examples and exercise sets, so no matter which one the students start with, they will see the connection to the other. Mark doctorVeryGood Wonder Book Frederick, MD Very Good condition. 5th edition. Issued without dust jacket. $2.99 +$3.99 s/h Good Virginia Social Ventures VA Norfolk, VA 2008 Hardcover0077224844
MAT-201 IDEAS IN MATH 3 Credits Mathematical models underlie decisions in science and industry and economics and business, and using mathematics to solve problems can improve our lives. The primary goal of this course is mathematical literacy – for the student to understand how mathematics is used in the world around us. The student will gain this broad understanding of contemporary mathematics through the study of the following specific topics. Course Objectives At the completion of this course, the student will be able to: Find Optimal Solutions using graph theory. Analyze and Manipulate Data to demonstrate probability and statistics. Identify and discuss various voting systems in terms of fairness and social choice. Use Game Theory to navigate conflict strategies. Discuss information science as it pertains to identification numbers, codes, and cryptography. Apply Dynamical Systems and Chaos to biological populations and management of resources. DETC: Distance Education and Training Council Accredited by the Accrediting Commission of the Distance Education and Training Council, which is listed by the United States Department of Education as a nationally recognized accrediting agency.
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University preparation: mathematics Try using our navigation bar across the top to find upcoming events, or use the search just below the navigation if you are looking for a specific upcoming event. This course prepares students for future study of mathematics at university level by developing an understanding and application of algebra, geometry and calculus. Students will practise effective techniques for studying mathematics as well as learning to read and write mathematics clearly and intelligibly. Students will also develop an appreciation of the patterns which arise in mathematics and how they are applied in a number of different subject areas. Before considering a University Preparation Course please review important information to determine if you are eligible for the Mature Age Entry Scheme and how to go about qualifying and applying. Still can't find what you're looking for?
97808058166ories of Mathematical Learning Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning. This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Universit Laval in Qu bec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning
Everyday Math for Dummies"...more" is intended to be a quick, enjoyable adult-oriented course in the aspects of math you need all the time. Whether you're looking for a refresher on math skills you might have forgotten or want to obtain math skills you never fully understood, "Everyday Math For Dummies" can help you discover the answers to all kinds of problems. "Everyday Math For Dummies" Finally make sense of your checkbookMaster the simplest tipping rules in the worldCalculate compound interest like an investment proUnderstand the math of refinancing and debt managementDecipher the fine print in a credit card agreementFigure percentages easily with a calculator, on paper, or in your headGet a handle on all that stuff from high school--algebra, geometry, and trig"Everyday Math For Dummies" can help you take charge of your life. Complete with a tear-out cheat sheet for you to keep handy for when the kids need help with their homework or you need help completing your tax return, this book makes math easy.(less) Paperback, 384 pages Published April 27th 1995 by For Dummies (first published April 13th 1995)
ALC62 Basic Math Skills Lab In conjunction with the instructor, students choose a limited number of topics in Basic Math (MTH 20) and/or Introductory Algebra (MTH 60 and 65) to review over the course of one term. Instruction and evaluation are self-guided. Students must spend a minimum of 60 hours in the lab. Completion of this course does not meet prerequisite requirements for other math courses. (For detailed information, see the Course Content and Outcome Guide ).
The following content is provided under a Creative Commons License. Your support will help MIT OpenCourseWare continue to offer high quality education resources for free. To make a donation, or to view additional material from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR STRANG: Okay. Hi. So, our goal, certainly, to reach next week is partial differential equations. Laplace's equation. Additional topics still to see clearly in 1-D. So one of those topics, these will both come today, one of those topics is the idea, still in the finite element world, of element matrices. So you remember, we saw those, that each bar in the truss could give a piece of A transpose A that could be stamped in, or assembled, to use the right word -- I think assembled is maybe used more than stamped in, but both ok -- into K. For graphs, an edge in the graph gave us a little [1, -1 ;-1, 1] matrix that could be stamped in. And now we want to see, how does that process work for finite elements. Because that's how finite element matrices are really put together out of these element matrices. Okay, so that's step one, that's half today's lecture. Step two, problem two now, coming from the next section, is fourth order equations. Up to now, all our differential equations have been second order. Are there fourth order equations that are important? Yes, there are. For beam bending. So I'll describe that application, which leads to fourth order equations. Do they fit our A transpose C A framework? You bet. You know they will. Each additional application in the framework kind of get us comfortable, familiar with that framework, what it can do. The A transpose C A. So let me start with element matrices. I'll get the homework, those numbers will get posted on the website later today. I just thought I'd put them down, and I have to figure out what would be a suitable MATLAB question. So my idea for this homework, as it really was for the last homework, was that you get some, not a large number of ordinary questions, paper and pencil questions, and one MATLAB question. When I wrote MATLAB last, people interpreted that as last MATLAB. But those words are not commutative. Right? I just meant -- and it doesn't really matter, it was a dumb thing to say -- I meant you to put the MATLAB question at the end after the regular questions. Sorry. So that MATLAB is due. Maybe a bunch of those turned in on Monday didn't include the MATLAB. No penalty. I'm talking now about the MATLAB for the trusses. How many have still got a MATLAB for the truss still to turn in? A number. Oh, not too many. Okay. Anyway, just when you can. In my envelope is good. Okay. So it'll be a similar thing for this week, and because it's short I said okay, let's get that cleaned up by Monday. And then we're ready for vector calculus, partial differential equations, two and three dimensions, the next big step. If I want to illustrate element matrices, the best place I could do it would be to go back to our piecewise linear elements in 1-D, and see how an element now is just one of those little intervals. Little pieces of the whole structure. If it's a bar, or whatever it is, I've cut it into pieces. Here's one piece, here's another piece. With finite differences, if I gave you unequally spaced meshes, if my little h is different from my big H, we'd have to think again. I mean there would be some three point, instead of minus one, two, minus one for the second difference. It would be a little lopsided, of course, when the mesh is unequal. We would have to think that through for finite differences; for finite elements, the system thinks for us. So I just want to show how that happens. So I'll take this. What's the element matrix for our standard equation for that element? Okay. And then it would fit into the big matrix K. I'm going to come up with a matrix K that I could do in any other way, but this is the way it's really done. So I look in that interval. I'm focusing on that interval. So here I've drawn the basis function. But now I'm not going to operate so much with basis function. Let me just think about that interval again. That's the same interval. So those were the basis functions that went up to height one. One started at height one and went down, one started at height zero and went up. But it's their combination, of course. Let me number this node number zero and this node number one. So we have some height, U_0, here. This is coming from U_0 times that hat. And some other height, U_1, here, which is coming from U_1 times that hat. But inside this interval, my U in this interval is U_0 times that first hat function, the phi_0, the coming down hat. Plus U_1 times the phi_1 function, the going up hat. It's a linear function, so it's going to be there. That's my graph -- no, yes. This is U(x). U(x). Okay. Right? I'm focusing inside one element. One interval. I've numbered them zero to one, but of course that distance is H. Okay, so there's my function. Right? Everybody agrees that this combination, it starts out right, it ends up right, at height U_1, and it's linear. So that's got to be right. So really, what's the contribution from that element? I look at the quantity, and I'm always taking the phi functions to equal the V functions. So I can write this as c(x) times dU/dx squared, dx. Over the whole thing, over the whole interval, that would be the U transpose K U. This, everybody remembers the K part, of course, comes from the left side of the problem. It comes from integrations. And this dU is now a combination of all the -- with weights U_0, U_1, U_2, U_3 -- if I plug in for capital U and do all the integrals, I'll see what K is. Now what's the point? The point is, when I did those integrals, the question is, how am I going to do the integrals? Do I do them the way I did before, was I watched what phi_0, one phi times another phi and I integrated. That was successful. But the new way is, integrate it an interval at a time. Do the integrals. So this would be K global. Now I'm going to go just from zero to H. If I go from just zero to H, that's going to give me the K element piece. The little piece that comes from this little interval. And on that little interval, this is my formula for U. I'm just hoping you'll sort of see this as a reasonable idea, and then when we do the integral you'll see it. It clicks. Okay, how does it click? So what's my plan? My plan is, here's my function. There is its picture. I'm just going to plug it into here. Oh, it's going to be simple, isn't it? What's the slope of that function in that element? On that interval? What's the dU/dx? So instead of doing every full integral for each separate phi, I'm doing every element integral for both phis. See, these two phis are both coming in to that element. Okay, so what's dU/dx. I didn't realize how neat this that's going to be. So what's dU/dx in this element? I'll use a different board here. So it's an integral, then, from zero to H of whatever my c(x) might be. And I'll make a comment on that. But my focus here is, what's dU/dx? What's the derivative? And then I'm going to square it. For this function, for that picture, the slope is obviously (U_1-U_0)/H Right? The slope is (U_1-U_0)/H. And I'm squaring it. dx. Okay. Let me take c(x)=1. Just to see clearly what's going on. So c(x) is just going to be one. Okay, so I'm claiming that this is my U transpose. My little piece. Why is it only a little piece? Because it only involves two of the U's. It's going to be a little two by two element matrix, that comes from this element. And then it's going to to be put into the big K, the global K, in its proper place. Okay, well. It's trivial, right? This is a constant, this is a constant, the integral is just H times U_1-U_0, squared, over H squared. Because that's getting squared, the interval was length H. I think I just have a 1/H. So this is my U transpose K element U. And now I want to pick out, what's that matrix? What's that little two by two matrix that only touches these two U's? What's the matrix -- well, since it only touches these two U's, you can tell me. I want a U_0, U_1. Sorry, let me make a little more space. And you can tell me what matrix goes in there. I want this all to match up. U_0, U_1. Now here is the two by two element matrix, . What's the two by two matrix that will correctly produce this answer? I'm just shooting for that answer. What do I have here? This is U_1 squared minus 2U_0U_1, plus a U_0 squared. Right? And I have to remember the 1/H, so it's automatically going to come out right. So there's a 1/H, shall I remember that first off. 1/H is part of my element matrix. And then, what are the numbers that go inside that matrix? We had practice with this. You remember when we talked about positive definite matrices, way back in chapter one? The point was that we could look at eigenvalues, or pivots, or something. But the core idea was energy. The core idea was that energy, that quadratic, and that's what we're looking at again. That's the energy. That's the energy, right there, and this is the energy, this is the energy in the finite element subspace. All I'm saying is, what matrix, what two by two matrix, goes with U_1 squared minus 2U_0U_1 plus U_0 squared. Just tell me what to put in that matrix. What do I put in here? One, right. Because it's multiplying U_0 U_0. What do I put there? Minus one. Good. Because I have a minus two, it comes in, minus one comes in twice, and a one goes there. So there, with the 1/H included, is K_e. K element, for that element. For the big H element. You'll say big deal, because we've seen this thing before. Notice what is nice. First of all, notice how nice that is. It's particularly nice, of course, because I took c(x) to be one. So let me make a comment. Suppose c(x) was not one. What would I do? Suppose c(x), suppose I have some variable stiffness in the material. Suppose the material could be changing width, so its stiffness would change. So in other words, I'd have a variable, c(x), that I should do the integral. Probably finite element systems aren't set up to actually do the exact integral. What would they do? They would take, for that simple integration, they would probably just take c(x) at the midpoint. So there's a numerical integration here in the creation of these element matrices. And numerical immigration is just, take a suitable combination of the values at a few points. You do know Simpson's rule? Simpson's rule, that's a pretty high level rule. My suggestion there was just a midpoint rule. Just take c(x) at the middle of the interval. Then it would factor out. So I should really put a c here. A c should really be coming in there. And you expected that, right, from the A transpose C A. We always saw a C in the middle. It really should be there. When I took c to be 1, I didn't see it. So what am I doing? I'm approximating c(x) by c at halfway. Approximately. I would replace this unpleasant, possibly varying, function by c at a point and use that value. So numerical integration is one part of the picture that we won't go into all the different rules. There's a rectangle rule, there's a trapezoid rule, very good. There's the Simpson's rule that's better. As I get higher order elements, like those cubic elements I spoke about, the numerical integration has to keep up. If I was integrating cubic stuff, I wouldn't use such a cheap rule. I would go up to Simpson's rule, or Gauss's rule, or somebody's rule. Anyway, that's the c part. Here's the part that stamps into the matrix. Notice, by the way, when I stamp it in, tell me how it's going to look stamped in. And then I've completed it. So here's my big K. I wish I had a little more room for it. Okay, here's my big K. So that interval that I drew there, the H interval, will stamp in here, some two by two. Right? Now where will the similar thing coming from this guy -- maybe it has to be numbered minus one. Sorry about that. That's another little interval. I'll do the same thing on that interval. I'll get a little element matrix, two by two guy, for K for that element. And where will it fit in to the big k? Does it fit in up here, let me just ask you. Does it fit in up there? Yes, no? I'm assembling, stamping in the small two by twos into the full n by n. And if I draw the picture you'll see it. So when I do the two by two for that big H interval, it goes there, let's say, then I just want to say where does the two by two go for the interval to the left? Does it go there? Nope. How does it go? It overlaps. Right? It overlaps. Why does it overlap? Because the phi_0, this guy, is acting on the right, and also acting on the left. The U_0 is active, is partly controlling the slope this way, and also that way. The U_0 is in common the two intervals. Anytime any unknowns, any mesh points that are in common to two elements, we're going to have an overlap when we assemble. And so it'll just sit, it'll sit right there. And so there is the diagonal guy. And maybe you could tell me what number will go there. What number would actually go there? And then you'll see the whole point of assembly, stamping in. Well, what number goes there from this? One times the c/H. So in here would be the c, can I call it c right, or c_H, c on the big H interval, divided by the H. Because that one, we had to get it right. And then what will go in that very same spot? So add it in coming from the small h interval. The same thing, it'll be this one, like shifted up, moved over. So it'll be coming from that one, so it'll be a c on the little h interval, divided by little h. That would be the diagonal entry of K. That's what we would see right there. Over here, should I write a typical row of K? Typical row of K, when I do that, is going to have this c_h/h, plus c_H/H. That's like the two, right? That's like the two. And what goes here? What will the entry be that sits there when I assemble? Just this guy. Right? Just this guy, times that. The entry here will be the minus c_H/H. That'll be the entry. This is the diagonal one, this is the one to the right, and what's the one to the left? What's the one here? Well, you know what it is. It's going to come from the minus and it'll be the minus c_h/h. Look at that. That just shows you how it works. And again, you can look at that, page 299 to 300 in the book. You see that if the c's are the same, if the h's are the same, then we're looking again at our minus one, two, minus one. Times whatever c over h, to keep it dimensionally right. Do you see that? It's just simple. Simple idea. The point is that each interval can be done separately. It's a simple idea in 1-D. It's a key idea in 2-D, where we have triangles, we have tetrahedra, tets. We'll see this in two dimensions, later in this chapter, when we're doing Laplace's equation. It's just fun to see it work. You'll have different triangles, say column triangles. So that phi -- do you want me to look ahead? Just ten seconds, to triangles? So imagine we have triangles here, so we have piecewise, we have little pyramids. Instead of hat functions, they grow to pyramids. So there's a pyramid guy whose height is one there, and drops to zero in all these places. And that's our phi. Our trial function, test function, will be pyramid function, then. And I can do integrals that way, or I can take the integral over a typical triangle. So a typical triangle is involved with three, now I've three functions, in the linear case, controlling inside that triangle. So what will be the size of the element matrix? Can you sort of see how the system is going to work? And then we'll make it work in 2-D. Every node, every mesh point, corresponds, has a pyramid function, has a U that goes with it. Those U's are the unknowns. And how many of those unknowns are operating inside that triangle? Three. So what will be the size of the element matrix, the non-zero part of the element matrix? Three by three. What else could it be? So we'll see what it looks like. And we'll have integrals over triangles. So that's good. Okay, thanks. Exactly halfway through the hour is exactly that first topic of element matrices. Done. Okay. Let me take two deep breaths, and move to fourth order equations. Fourth order equations. For the bending of a beam. So I'd better draw a beam. This is a 1-D problem, still. This is a 1-D problem, still. To keep it 1-D, this better be a thin beam. So this is a thin beam. And the loads, what's the difference? What's here? It looks like a bar, pretty much, right? But the difference is, the load is acting this way. The load is acting that way on the beam. Maybe two loads. Maybe a uniform load. Maybe the weight of the beam. But it's transverse. It's in the perpendicular, it's transverse to the beam. It's this way. So the beam bends. Let me do a fixed free. So this'll be a fixed free beam. Fixed free, the word for fixed free would be cantilever beam. Okay. So what happens if I impose those loads. Well, the beam bends. So the displacement is now downwards, is now not the direction of the rod, the displacement I'm interested in is perpendicular to the beam. Downwards. Okay, so we can start on our framework. So this is displacement. u(x). I'll stay with the same letters. So you know I'm going to have an A, that will take me to whatever this is going to get called. What's the quantity there? It's going to be, let's see. What happens? So this is just geometric now. Let me put in the easy part, C. That'll be sort of the bending stiffness. Right? This'll be the bending stiffness. Because the beam is going to bend. And over here I'll get a suitable w. So when the beam bends, it's curvature. Curvature of the beam is what's produced. It's not stretching of the beam; it's curving of the beam. So this quantity, e, will be the curvature that comes from the displacement. If I displace these beams, suppose I put a node here, it's going to bend that down. The bar will curve. So the curvature, e. Now then, the question is, what is this A; what is the curvature? Well, do you remember? You're on the ball if you remember the formula for curvature. It's a horrible formula, actually. But that's only because we're going to make it better. You remember the curvature, it was in calculus. Yes, you all remember this. Suppose I have a graph. I know its slope, that's become easy now, right? Calculus. But the curvature of it, what derivative did it involve? Second derivative. And was it the second derivative exactly? No, unfortunately there's some term which is horrible. One plus the first derivative squared, all square root. But I'm just going to take u double prime. So this is an approximation. So what is A now? What's my matrix, A, that gets me from u -- or my operator, A, that gets me from u to e? What's the e=Au equation? A is just second derivative. That's something new. A is second derivative. And why do I do that? Because I assume small curvature, small displacement. I assume that u' squared is very small compared to one. So it's just slightly bent. A beam that goes way down here, I'd have to go nonlinear. But if I want to keep things linear, I approximate this will be much smaller than this, so one is fine that term goes. And now the next step will be easy. What's the bending moment? This will be called the bending moment. And let me use the letter w again. I should really capital M for bending moment. That will be the stiffness times the curvature. So that's the force, the way the spring had a restoring force by Hooke's law. This is the equivalent of Hooke's law. But this restoring force is not pulling back, it's bending back. It's torquing back. And then, of course you know, there'll be an equilibrium equation to balance the load. So this load is the f(x). And you know what that'll be. Because you know it'll involve A transpose. And the transpose of that, do you want to just make a guess? I shouldn't use transpose, of course, but I'll use it again. It'll be the same; it'll be second derivative. I mentioned we had a minus sign with the first derivative, but now we're going to have two minus signs, so it's going to come out symmetric, second derivative, and the equation here will be w''=f(x). Our framework is working. We have plus boundary conditions on u. And here we have plus boundary conditions on w. So those parts we have not yet mentioned. And of course, that depends on my picture. While we're at it, why don't we figure out, what do you think is the boundary condition here? And how many boundary conditions am I going to look for all together? Four all together. Because I have a fourth order equation. There will be four arbitrary constants until I plug in boundary conditions. So I'm looking for four boundary conditions, two at this end, two at that end now. And what will be the two at the fixed end? At the fixed end, obviously, it's built in. Built in. Slightly different words sometimes for the beam problem. Here I'll have u=0 and u'=0. Those apply with A; those go with A. Those are the essential conditions, the Dirichlet conditions, the ones I must impose all the way. And now at this free end, what do you think? Well, it's great. It's w=0, and w'=0. It's just beautiful, the way it all works. So that's a completely fixed free. Then why don't I draw in, just while we're talking about boundary conditions, an alternative. So here's my beam. And now you see, it's under a load, f(x), transverse load. Now that would be different boundary conditions. Anybody know the name of a beam that's set up like that? Simply supported. You don't need beam theory, and I don't know beam theory, to tell the truth, to do these problems. So that's a simply supported beam. And what are the boundary conditions that go with that? Well this is u=0. No displacement, it sits there on that support. And what else is happening at that support? There's no bending moment. Nobody's here. Right? So it's w=0. And at this end, too. Also at this end, u(1) is sitting there, and w(1) is zero. Yeah. That would be the boundary conditions, four of them, for a fourth order equation that we'll just write down in a minute, for simply supported. And we could have a mix. This could be simply supported here, free here. I think. Or maybe, could it be, or maybe that's too risky. Would that be a singular case, simply supported? Huh. So as always with boundary conditions, some are unstable. Some are not going to determine all four constants. Just the way free free didn't work, right? Free free for a rod didn't determine anything, it left a whole rigid motion. Maybe u=0, w=0 at one end, and free at the other end; it sounds risky to me. But we can see. Okay. So, do you get the general picture of the beam? So what's the equation? What's A transpose C A, when I put it all together? I'll use that space to put in A transpose C A. Continuous, we're talking here. Right now we've got differential equations. So what's the differential equation, A transpose C A? So it's the second derivative. I'm just going backwards around the framework, as always. The second derivative of this, and this is c(x) times e(x), and e(x) is second derivative of u=f(x). Good. In ten minutes, we've written down the framework, some possible boundary conditions, and the combined A transpose C A equation. I mean, we're ready to go. We've got the pattern to think about this. So let's see, what should we do first? I would say the first thing to do is, let c be one and solve some problems. Let c be one, and consider -- so if c is one, it's a fourth derivative equation. Should we take uniform load? Yeah. How does a beam bend under its own weight? So it's just one, or whatever constant. So it's constant load, it's just its own weight, it's going to sag a little in the middle. What's the solution to that equation? And what shall I take as boundary conditions? Let me do the simply supported one. Because that would be kind of nice. So it's simply supported, it's sagging under its own weight, with u(0)=0, u''(0)=0, because that's the w. And u(1)=0, u''(1)=0. Whatever. I don't know that I'll have the patience to go through and plug in all four boundary conditions to determine all four constants. Just get me to that point. Get me to a solution u(x), the general solution here that's got four constants in it is what? Okay. Okay, think again. What are we looking at? We're looking at a linear differential equation. Linear problem. I'm asking for the general solution to a linear equation. What's the general set up? General set up is, particular solution plus nullspace solution. Right? You see an equation like that, looking for the general solution, tell me one particular solution and then tell me all the solutions when it has zero on the right, and we've got everybody. So that was true for matrices, it was true for Ax=b, it's just as true for differential equations. So what's one particular solution? What's one function whose fourth derivative is one? Yes? What am I looking for here? 1/4 of x to the -- no, what? 1/24, is it? 1/24 of x to the fourth? x to the fourth over 24. Because four derivatives -- so we're thinking we're in the polynomial world here. Just as we were with u''. With the bar it was x squared over two, the particular solution, now we're up to x fourth over 24. So that's the fourth derivative is one, good. So I'm seeing a fourth degree bending there. And now what about the null space solutions, the homogeneous solutions. This accounts for the one, now what are the possibilities if it was a zero? You're going to tell me the whole bunch, right? A plus Bx plus Cx squared plus Dx cubed. Because all of those have fourth derivatives equal zero. So that's the general solution. Okay. So whatever the boundary conditions are, they determine A, B, C, D. We're not that far away from Monday's lecture on fitting cubics. Actually we're really close to it. When we use finite elements, we're going to use exactly those cubics. I'll get to that point. Let me take the other model problem, that everybody knows what's coming. What's the other right hand side that this course lives and dies on -- lives on. Delta function. Right. Delta at some point. So that's a point load then. I can make it whatever the boundary conditions are. Right. Good point. This boring stuff will just repeat, right? That's the null space solution. But now, what is a particular solution? The particular solution has become interesting. The particular solution here was straightforward, simple, a good one to do first. What's a particular solution to a point load? So instead of having distributed load here, I'm putting a heavy weight here at this point, a. And it's heavy weight, I'm multiplying the delta function by one, I could multiply by some l for load or something, but let's just keep it simple. What's a solution to that? Fourth derivative equals delta. So that means I've now got to integrate, one way to get the answer here would be to integrate four times. Right? If I integrate delta four times, then I've got something whose fourth derivative will match delta. So do you remember the integrals of delta? Okay, so I integrate. First integral is, step. Second integral is, ramp. Third integral is, quadratic, right? This was linear, boop boop, linear pieces. The next integral is going to bring me up to quadratic ramp. And the next, fourth one is going to bring me up to cubic ramp. Cubic. So it's going to be cubic ramp, is what I get there. So one particular solution would be a function that's zero, and then at the point a, it suddenly goes up cubically. So it's zero here, and it's x cubed over six there, I think. If I do integrate three times, I'll be up to x cubed over six. Is that right? Yes, cubic. So that's an interesting function. Of course, these parts will tilt the function, will change it. So our solution won't look like this, because I've only got one particular function, and I'll need these to satisfy the boundary conditions. So there is one particular solution. The general solution -- yes, good for us to think out the general solution. What does that picture look like when I add in this stuff? Very, very important. I'm sorry I don't have more space for this highly important picture. Okay, so here's my point a. Keep your eye on that point a. Okay, so to the left of it, I've got some curve, whatever, dut dut dut dut dut, the beam. And to the right of it, I've got some other curve, whatever it is, dut dut dut dut dut. And what's cooking at point a? What's the jump condition at point a? That's the critical question. What changes at point a? You remember, this is the corresponding thing, the analog of our ramp. So what changed for the ramp at point a? What jumped? The slope. Okay, now the question is what's going to jump here? What jumped there? Here, did the function jump? Certainly not. Did the slope jump? Certainly not. Did the second derivative jump? No, no. The second derivative was zero and then zero. What jumped? Third derivative. The third derivative is allowed to jump. And of course. A jump in the third derivative produces a delta in the fourth. Right? It just works. So this is a cubic of some sort, coming from that jump. This is another, a different cubic, coming from this sort, from this junk, and this. So it's cubic in each piece. Why is it cubic in each piece? Because, what's the equation in the middle of that piece? What's our differential equation if I look here? Here's my equation. What is it in the middle of that piece? u fourth equal zero. The delta function is zero there. And u fourth is zero here. So of course this is a cubic spline. We're meeting that neat word, cubic spline. Those turn out to be very, very handy functions for other things, too. So we see them here as a solution to fourth order equations with point loads are cubic splines. Because the big key point is that there's a jump here in u''', the third derivative. A jump in the third derivative, that's what we saw here. And we'll see it if we have any cubic meeting any cubic. Let me just say, a jump in the third derivative, your eye probably won't notice it. I mean, it's a discontinuity, somehow. We don't have the same polynomial from here to here. But that discontinuity in u''', it's pretty darn smooth still. The slope is continuous, so your eye doesn't see a ramp. And even more, the curving is continuous, the curvature is continuous. e and w are good. It's just a jump in the third derivative. Okay, so I want to speak about splines, and more about this, and about finite elements for beam problems on Friday. And then that will take care of 1-D and we'll move into 2-D. Okay
Thinking Mathematically, Expanded-/two-term course in liberal arts mathematics, or survey of mathematics. This Expanded Edition of Thinking Mathematically includes additional chapters on Voting and Apportionment, and Graph Theory. More than any other course/text, Liberal Arts Math depends on strong, engaging applications and examples. Bob Blitzer's books are highly acclaimed for their well-conceived, relevant applications and meticulously annotated examples. This highly anticipated revision achieves the difficult balance between coverage and motivation, while helping ... MOREstudents develop strong problem-solving skills. This book provides students with the skill building and practice so crucial at this level as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics as they move forward in their college careers and beyond. Provides readers with the skill building and practice that is so crucial as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics. For anyone interested in refreshing his/her fundamental math skills. Softcover.
Professional Commentary: Students?model successive discounts as a composition of functions and show that, in general, function composition is not commutative. They study the graphs of the discount functions to find the values for which?different orders of successive discounts yield equal results.?An activity sheet, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included.... Professional Commentary: Students use graphs, tables, number lines, verbal descriptions, and symbolic representations to analyze the domains of various functions. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included.... Professional Commentary: Students must find the value of a composition of functions by looking at the graphs of the functions. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP).... Professional Commentary: Students must determine the value of a function by looking at its graph. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP).... Professional Commentary: This item asks students to evaluate the composition of a quadratic function with a linear function for x=2. This multiple-choice question is a sample test item used in grade 12 in the 1992 National Assessment of Educational Progress (see About NAEP).... Professional Commentary: Students are asked to find the composition of two functions. This constructed-response question is a "hard"?test item used in grade?12 of the 2005 National Assessment of Educational Progress (see About NAEP).... Several real-world situations motivate the study of linear functions, their parameters, and behaviors. The contextual situations lead to the abstraction of function and provide tools for understanding and long-term memory....
What about spelling, grammar, and syntax? - 3.5 Min. MP3 What about Latin and Greek? - 2.7 Min. MP3 What feedback have you had from users? - 2.3 Min. MP3 What is the most common objection you hear? - 1.4 Min MP3 Christianity in the curriculum - 1.3 Min MP3 Academics and faith in the curriculum - 1.7 Min MP3 In this rare interview Dr. Robinson speaks with John Saxon, the author of the Saxon Math books we recommend for use with the Robinson Curriculum (RC customers can get these books from OISM at our cost). The interview is full of great insights into what makes this math program so effective and essential to your homeschool. "Understanding more often than not follows doing rather than precedes it. If I'm going to teach you how to drive, I don't lecture you on the theory of the internal-combustion engine. I get you behind the wheel of the car and drive around the block." - John Saxon This interview is the only audio of John Saxon available today and presents a rare and unique opportunity to hear the real story of Saxon Math from the author himself. The value is further enhanced by Dr. Robinson's insights on how to maximize the benefit of Saxon Math by using it in a self-teaching homeschool using the Robinson methodology. All of the files presented here and more are now available on this combination Audio and Data CD. You get about one hour's worth when you play it on your regular CD player; put it in your computer and you get another 7 hours or so with a super easy-to-use, goof-proof guide to everything. One special item is the Preparing for University speech Dr. Robinson gave in February 2004 in Beaver Creek, Oregon, a must-have for parents with older students. You also get some tracks of Art Robinson talking with some homeschoolers in a relaxed family room setting you won't find anywhere else. Its great for new users, RC veterans, and newcomers wanting to know what its all about. It also contains a printable version of this website for your off-line friends. Let us know if you need more than one as quantity discounts are available.
Arthur Mattuck: Introduction to Analysis The book was developed at MIT, mostly for students not in mathematics having trouble with the usual real-analysis course. It has been used at large state universities and small colleges, as well as for independent study. Students evaluate it as readable and helpful. The current printing, by CreateSpace and at a reduced price, is the eighth, incorporating all known significant corrections and a new Appendix F. General description This book is meant for those who have studied one-variable calculus (and maybe higher-level courses as well), generally skipping the proofs in favor of learning the techniques and solving problems. Now they are interested in learning to read proofs, and to find and write up ther own: perhaps because they will need this for the next steps in their chosen field, or for intellectual satisfaction, or just out of curiosity. There are two paths to this. Some books start with a great leap forward, giving the definitions in n-space. This requires first an excursion into point-set topology, whose proofs are unlike those of the usual calculus courses and are a roadblock to many. The path chosen by this book is to start like calculus does, in 1-space (i.e., on the line) and focus on the basic definitions and ideas of one-variable calculus: limits, continuity, derivatives, Riemann integrals, and a few more advanced topics. It's done rigorously, but also in as familiar a way as possible. So from the start it will use as a source of examples what you know (with occasional reminders): K-12 mathematics and basic one-variable calculus, including the log, exp, and trig functions. This takes up about two-thirds of the book, and might be as far as you wish to go. It sounds like this is just repeating calculus, but students say that it feels very different and is not all that easy. The rest of the book gets into techniques from advanced calculus based on the notion of uniform convergence, and usually used in lower-level courses without proof: differentiating infinite series term-by-term, and differentiating integrals containing a parameter (the Laplace transform, for instance). For the latter, it's finally time to learn about point-set topology in the plane (i.e., 2-space, but n-space is no harder). There's also for the curious or needy an optional chapter with the most important facts about point-sets of measure zero on the line, and a more powerful integral: the Lebesgue integral. Two appendices respectively provide needed and optional background in elementary logic, and four more give interesting applications and extensions of the book's theory. (See below for the link to the Table of Contents for more details about the topics and the order in which they are given. Generally helpful features --- Leisurely exposiion, with serious comments about proofs, other possible arguments, writing advice; some semi-serious comments, too; --- Attention paid to layout and typography, both for greater readability, and to give readers models they can imitate; --- Questions after most sections of a chapter to firm up what you just read, with Answers of various sorts at the end of the chapter: single words, hints, complete statements, formal proofs. (See below for the link to Sample Text Pages to see examples.) Mathematically helpful features --- The language of limits is simplified by suppressing the N and the delta when their explicit value is not needed in the argument, replacing them with standard applied math symbols meaning "for n large" and "for x sufficiently close to a". These are introduced carefully and rigorously; some caution is needed, which is described at the end of the Preface (see the link below to it). --- The book tries to go back to the roots of real analysis by emphasizing estimation and approcimation, which use inequalities rather than the equalities of calculus, but have a similar look, so that many proofs are calculation-like "derivations" that seem familiar. But inequalities require more thought than equalities; they are often mishandled and warnings have to be given and repeated. Looking at the book For more details about what's written above, you can use these links in order to get an idea of how it's written, and what studying analysis from it will be like. These are a few sections, totalling about 15 pages in all, showing text material, Questions, Exercises, and Problems, to give you a sample of the mathematical writing style and level. They are selected from the first three chapters: --- Chapter 1: Real Numbers and Monotone Sequences --- Chapter 2: Estimations and Approximations --- Chapter 3: The Limit of a Sequence Information about earlier printings PRINTING: There is only one edition so far, but several printings. The printing is identified by a number sequence like 10 9 8 7 6 5 4 on the left-hand page facing the dedication page; the sequence shown identifies the fourth printing, for example. CORRECTIONS: The current inexpensive printing is the eighth; it incorporates all the significant mathematical corrections needed from earlier printings. I would be grateful to hear about any further corrections needed. as teacher or student; write to: mattuck@mit.edu For those using printings earlier than the eighth, here are lists of corrections. Bullets indicate the more significant ones; none are major. Mathematical corrections to the Third through the Seventh Printing ( pdf file ) Mathematical corrections to the Second Printing (see also the corrections to printings 3-7 above) ( pdf file ) Mathematical corrections to the First Printing (see also the corrections to printings 2 and 3-7 above) ( pdf file )
Intermediate Algebra Designed for first-year developmental math students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra owes its ...Show synopsisDesigned for first-year developmental math students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra owes its success to the hallmark features for which the Larson team is known: learning by example, accessible writing style, emphasis on visualization, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and understand the content. The new Student Support Edition continues the Larson tradition of guided learning by incorporating a comprehensive range of student success materials throughout the text. Additionally, instructors and students alike can track progress with HM Assess, a new online diagnostic assessment and remediation tool from Houghton Mifflin
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Other Courses Home Schooling Maths / GCSE Mathematics – The Course The GCSE Maths course gently guides the student through basic mathematical skills, progressing onto more advanced material as the student's skills and abilities develop. The course is divided into two parts: the first is for all students; the second is for those who will be taking the Higher tier of the examination. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall programme of study. Effective learning is encouraged through frequent activities and self-assessment questions. There are thirteen tutor-marked assignments and a practice exam paper.The course covers the entire syllabus in 13 modules, with a 14th on the examination. The Syllabus Our GCSE Maths course prepares students for AQA GCSE Mathematics syllabus 4365 for exams in 2014 and later years. We have chosen this syllabus as it is the most suited to distance learning. Assessment for 2012 is by two written papers. Paper 1 (non-calculator) is worth 40% and Paper 2 (calculator) is worth 60% . Special Requirements A reasonable level of proficiency in arithmetical skills is assumed. Coursework No coursework or controlled assessment is required. The AQA 4365 specification contains an emphasis on "problem"-solving – that is to say, questions are more likely to be given a "real world" context. This should make them easier to grasp and visualize while the underlying mathematical skills remain the same.
solve it; a new aspect of mathematical method. This title presents a demonstration of how the true mathematician learns to draw unexpected analogies, tackle problems from unusual angles and ...Show synopsisThis title presents a demonstration of how the true mathematician learns to draw unexpected analogies, tackle problems from unusual angles and extract a little more information from the data. It is a collection of truly practical lessons.Hide synopsis Description:Good. Some creases to the corners and wrinkling and soiling to...Good. Some creases to the corners and wrinkling and soiling to the outer pages. Most of the book and text is clean and all unmarked. Description:New. This item is printed on demand. George Polya was a...New. This item is printed on demand. George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems, " wrote Polya, "is a practical art, like swimming
Buy Used Textbook eTextbook We're Sorry Not Available New Textbook We're Sorry Sold Out More New and Used from Private Sellers Starting at $6 Graphical Approach to College Algebra Graphical Approach to College Algebra, A Graphical Approach to College Algebra, A Summary This major revision reflects the authors combined years of experience as classroom teachers, and underscores their enthusiasm for the use of the graphing calculator as a teaching tool. Their approach is to present the various classes of functions, examine the nature of its graph, and discuss the analytic solution of equations based on that function. Then, graphical support for the solution is provided with a graphing calculator. Using graphing technology to study math has opened up a new area of error analysis, so the authors have included a What Went Wrong feature to discuss typical errors. Throughout, the accent is on using both analytical and graphical methods to solve interesting applications for various functions. The new edition also includes a reference chapter on basic algebraic concepts for those needing a refresher course. Table of Contents Rectangular Coordinates, Functions, and Analysis of Linear Functions 1 (120) Real Numbers, Logic, and Coordinate System 2 (10) Introduction to Relations and Functions 12 (14) Linear Functions 26 (18) Equations of Lines and Geometric Considerations 44 (15) Solution of Linear Equations; Analytic Method and Graphical Support 59 (13) Solution of Linear Inequalities; Analytic Method and Graphical Support
Functions, Calculus Style. Graphs. A Field Guide to Elementary Functions. Amount Functions and Rate Functions: The Idea of the Derivative. Estimating Derivatives: A Closer Look. The Geometry of Derivatives. The Geometry of Higher-Order Derivatives. Chapter Summary. Interlude: Zooming in on Differences. Areas and Integrals. The Area Function. The Fundamental Theorem of Calculus. Finding Antiderivatives by Substitution. Finding Antiderivatives Using Tables and Computers. Approximating Sums: The Integral as a Limit. Working with Approximating Sums. Chapter Summary. Interlude: Mean Value Theorems and Integrals. Text is clean, no writing or highlighting. Some pages have water damage near the top. $8.73 +$3.99 s/h Acceptable Elusive Books Thornton, CO 2001-11-14 Hardcover Fair Text is clean, no writing or highlighting. Some pages have water damage near the top. $8.75
Parabolas and Quadratics Links to many lessons and activities, to be used in Algebra 1, Algebra 2, and with math teachers, including three paths to the quadratic formula. Look at everything, and decide what goes where for you, as the headings are merely guidelines. Mostly Algebra 1 A manipulatives-based complement to this work (or to any work on quadratics) can be found in my book Lab Gear Activities for Algebra 1. (Send me e-mail if you need help locating a copy.) The manipulatives make factoring and completing the square accessible to the vast majority of Algebra 2 students, while giving them a geometric perspective which is unfortunately missing from many curricula. That approach is all the more important if you teach this material to students in grades 7-9. - Sample activity from the end of the book, which makes a connection between the Lab Gear and graphical representations of certain quadratics (PDF). Mostly Algebra 2 The lessons below (in PDF format) involve the sparing use of the graphing calculator. Unlike some other calculator-based approaches ("graph this, graph that, what do you notice?") this is a rather theoretical unit, which helps develop students' symbol sense and goes for a lot more depth of understanding than is customarily expected at this level. Calculus Mostly for Teachers Late in the Math 1 / Algebra 1 course at The Urban School, where I used to work, we ask students to create a short report explaining the connections illustrated here, using their own example. One year, while grading this assignment, it hit me that there must be a new proof of the quadratic formula based on this, and sure enough, there is. You can read it in my article in the February 2008 issue of The Mathematics Teacher, under the title "A New Path to the Quadratic Formula". The proof involves neither parabolas nor completing the square! See an online presentation of the proof. [Let me know if it doesn't work on your computer.] For better results, including animations, download the file (3.2 MB), in .mov (Quicktime) format. Either way, grab a pencil to follow the argument, and click your mouse to advance through the slides. Parabolas are a major topic in secondary school, and yet in the US, students and teachers do not often think about them as geometric objects. This may be a consequence of the strict division between algebra and geometry courses. As a result, many basic properties of parabolas are not well understood. These pages present some key concepts in this domain:
In this course, you will learn about systems of linear equations, matrices, determinants, vector spaces, linear transformations, and eigenvalues. You will also improve your quantitative reasoning and develop your deductive logic skills. It is absolutely crucial that you take the initiative in the course. The best way to learn is by DOING, not by watching. So while an important component of the course is reading the text and watching the slideshows, the most important part is the homework exercises. There are 2 proctored exams in this course. You are expected to take your examinations at one of the NVCC campus Testing Centers. Be sure to allow enough time to complete your exam before the Testing Center closes; Testing Centers have specific policies relating to the administration of ELI exams. You will need to take a photo ID, your NovaConnect empl ID number, and the appropriate Exam Pass when you go to the Testing Center. This is an Extended Learning Institute (ELI) course. ELI courses differ from campus courses in several important ways, including enrollment dates, communication with faculty, assignment completion requirements, and exams. You must follow ELI's policies and procedures if you take this course. Read (or review) ELI's Policies and Procedures before you begin the course. If you have questions, call ELI at (703) 323-3347 or (888) 435-6822. 1. Use your web browser to connect to Follow the directions to determine your email, Blackboard and VIVA account user names and passwords. 2. Access your email account and make sure you know how to use it; you will be required to use this account for all course-related email. 3. Log on to Blackboard at 4. Click on this course under "My Courses." Review the entire course to make sure you understand what will be required of you. Then start completing the assignments. Please note that account generation takes approximately one week from the time of your paid registration. If you cannot log on after one week, contact the IT Help Desk. If you can log on to Blackboard, but your course isn't listed, please contact ELI or your instructor.
0321620917 9780321620910 Intermediate Algebra for College Students:The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process. Back to top Rent Intermediate Algebra for College Students 8th edition today, or search our site for Allen R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson.
Today's Students, Mathematics, and Society's Need Nowadays secondary school students must prepare to live in a society that requires a significant understanding and appreciation of mathematics. Managing in the real world would be difficult if not impossible without the necessary knowledge, skills, and applications of mathematics. The demands of society require much more of secondary school mathematics students than merely being able to compute the total of a grocery bill or determine whether a personal checkbook is balanced. Students must be able to apply mathematical skills to real-life problem-solving situations. For example, important principles in probability and statistics may be connected to the physical world, which may require individuals to collect, record, interpret, analyze, communicate, and represent data sets crucial to their decision-making processes. The interpretation of a graph as part of a medical diagnosis may influence a vital decision involving the health and well-being of an individual. Key concepts in numeration and algebra may help facilitate important personal financial decisions. The use of mathematical design enables the ongoing growth of computer technology, including the continued research and development of hardware, software, and further advancement of the Internet and telecommunication services. Careers and occupations in computer technology, business, the sciences, and engineering necessitate a more intense and multifaceted mathematical knowledge base than in the past. According to John Glenn, former astronaut and U.S. Senator, mathematics and science will also supply the core of knowledge that the next generation of innovators, producers, and workers in every country will need if they are to solve the unforeseen problems and dream the dreams that will define America's future (U.S. Department of Education, 2000).
Functions and Change: Model Approach to... 9780618858040 ISBN: 0618858040 Edition: 1 Publisher: Houghton Mifflin Company Summary: Intended for precalculus courses requiring a graphing calculator, Functions and Change emphasizes the application of mathematics to real problems students encounter each day. Applications from a variety of disciplines, including Astronomy, Biology, and the Social Sciences, make concepts interesting for students who have difficulty with more theoretical coverage of mathematics. In addition to these meaningful applicat...ions, the authors' easy-to-read writing style allows students to see mathematics as a descriptive problem-solving tool. An extended version of the successful Functions and Change: A Modeling Approach to College Algebra, this text includes three chapters of trigonometry. Crauder, Bruce is the author of Functions and Change: Model Approach to..., published under ISBN 9780618858040 and 0618858040. Nine hundred Functions and Change: Model Approach to... textbooks are available for sale on ValoreBooks.com, one hundred sixty five used from the cheapest price of $87.80, or buy new starting at $104.97.[read moreThe course was great at giving concrete, real world examples. Actual data was used so you could understand why you were learning the material, and that makes a big difference in your understanding. The many examples help students learn for themselves the material. The section on logs and exponentials really needs some beefing up with more basic abstract work. Too little time was spend on those subjects.
My daughter loves this book! It not only teaches the principles of Algebra, but teaches why it is important to know it and how to use it in everyday life. It has made Algebra so easy for her, that she said she wants to do ALL of her schoolwork this way. She was so disappointed to find out that Geometry is not offered by this company. I hope Alpha continues to add to the courses they offer! We also ordered the Spanish 1 book and are currently getting started on it. Share this review: 0points 0of0voted this as helpful. Review 2 for Teach Yourself Algebra 1 in 24 Hours Overall Rating: 5out of5 This item has directions you can understand Date:November 3, 2011 trish Location:Ottawa Kansas Age:45-54 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 I have returned to school after graduating thirty years ago. I never took algebra in high school. This book breaks down the problems,so it can be understood. I have always struggled with math and I find this product is working for me.
14 Total Time: 3h 27m Use: Watch Online & Download Access Period: Unlimited Created At: 07/23/2010 Last Updated At: 08/29/2013 Is your state committed to teaching the Core Standards this year? Some are, some aren't. Either way, this Algebra video introduces Algebra using a concrete and simple manner.Certainly most of the topics are in Common Core. But "basics are basics". You cannot be successful at math without them. What makes this Algebra help different? What makes it work? Here Algebra is taught by a National Board Certified Teacher using methods designed for those who really struggle with easy math. It is repetitive but not boring. The lessons are long enough but not too long. The practice is made for you to print out and work until you really get it! And always go at YOUR pace, not someone else's. These Algebra videos are for you IF you want to learn Algebra from the very, very beginning, if you are a real beginner. The lessons are clear and simple, and designed to relieve "math stress" and frustration. You can "watch online" OR "watch online AND download" to your computer. When you buy the series you get to choose. There are no time restrictions. They are yours forever. You may share them with your friends if you'd like. That would be a good thing! These math videos don't go too fast and you can pause them anytime you need to. If you want to listen to one part over again, just stop it, back up, and listen again. Even though you "get it" the first time you hear it, repetition is one of the best ways to learn. When you play the videos, download the PDF and work the problems right along with me. Then download the "practice on your own" sheets. The answers are provided for you to check your work. It will help you if you will go over and over the material. There are 14 Algebra video lessons in this Beginning Algebra Series. They range from 12-24 minutes each for a total of 3 hours 27 minutes. It's best to focus on one lesson until you really understand it and finish the practice downloads. Don't leave a lesson until you have mastered it. I suggest you watch the videos in this order but it isn't completely necessary. How To Combine Like Terms (Add/Subtract) How To Multiply in Algebra Integers And Number Line Multiplying Positive/Negative Numbers (2 Videos) Adding Positive/Negative Numbers Solving One Step Linear Equations Solving Two Step Linear Equations You may find cheaper math help or even free lessons on certain topics. I do not believe you will find better quality instruction. You may further check out my award winning credentials and testimonials at Below are the descriptions for each of the lessons included in the series: How To Add Like Terms Remember back in elementary school when math made sense? This video helps you feel that way about math again. Starting with "adding like terms", you can build a strong foundation so you can understand math from now on! Learning to "add like terms" is one of the first things you learn in Algebra. This algebra video lesson explains addition in a way that anyone can understand. When you need Math help, it is best to start with something you already know. Since it's easy to understand addition in Arithmetic, this video starts there and shows you how much Algebra is like Arithmetic. I repeat things a lot because I know that helps. You need to practice a lot because that helps too. Print out the Guide and Practice along with Answers for you to check your work. If you've never done Algebra before, this is a good place to start! It is fail-proof. Learn To Multiply in Algebra Just like in Arithmetic, you have to Add, Subtract, Multiply, and Divide in Algebra. It's not really harder, it's just different. This video shows you how to multiply. It shows you the signs, the symbols, and the terminology. It doesn't confuse things with negatives. That comes later. Print the Guide to work as you watch the video. Then print the Practice for....you guessed it...more practice. I challenge you to "get better" at Algebra by practicing, practicing, practicing. Okay? Give it a try. You'll be glad you did. What Are Integers Anyway? This video will show you exactly what integers are! Arithmetic uses only positive numbers and zero. Algebra uses negative numbers too! This is a big deal! Since Algebra uses "integers" all the time you really need to know everything about them. The number line is a picture of the real numbers. You will see the difference in counting numbers, whole numbers, and integers. The number line is the basis of all rules involving integers and is essential to add, subtract, multiply, and divide with positive and negative numbers. If you've studied Algebra before you know you must know your sign rules. I will explain them to you with a number line. Once that makes sense, then the rules are nice shortcuts to know. Remember it takes a lot of practice and that is where you come in. Work along with me as you watch the video and continue to practice until you are an expert yourself! Print the Practice and Answers and try my Fail-Proof approach. Repeat, Repeat, Repeat until you can teach it to someone else. Multiplying Positive And Negative Numbers This video is about the "M" word. I hate telling students to memorize something but this time....that's the truth. You have to memorize these three rules. If you want to be successful in Algebra you must learn to add, subtract, multiply, and divide with positive and negative numbers. This video shows you how these rules work and how to use them. As you watch this video, make sure each step is clear to you. If it is not, pause the lesson, rewind, and watch again. Download the PDF and work right along with me. In the end you will know these rules "as well as you know your name". That is what it takes to move forward with a good foundation. The best math help you can find anywhere allows you to work at your own pace, encourages repetition, and talks to you 1:1. That is what this video offers you. Multiplying Positive and Negative Numbers Cont'd Once you learn the signs laws for multiplying by heart, you can learn to handle more complex problems. This video is a more in depth look at multiplication. Whether you are multiplying fractions and any number of terms, it is easy to apply the rules, once you know them! It takes practice with these problems until they become second nature. You will learn a few shortcuts which you can use, not only to save time, but to check your problems and catch sign errors. Since one sign error can ruin an entire problem, you have to "get" this or forever fail Algebra. That's the cold hard truth. Work the problems along with me and keep practicing. That is the way to success. Adding Positive and Negative Numbers Note: You can buy just this lesson or the entire series. I'm just going to tell you the truth. You must be able to work with negative numbers or you will never get good at Algebra. On this video I show you how to combine positive and negative numbers. First I explain it the long way so you can add integers even if you don't "know your sign rules". However, you will get very tired of having to do everything the looooong way. That's why there are rules, or shortcuts. You'll love the rules because they will save you so much time! But first you must understand where they come from and then... learn them 'by heart'. You will be a much better Algebra student once you know the sign rules. Until you know them really well, you will struggle. Watch my video and I will explain how they work and why. You will understand. I make it easy. LOL. This is where it all starts. Once again, this video lesson is great math help whether you are brand new to Algebra or just reviewing the subject to pass a test or go back to school. This video is the most important one to help you move into more advanced math topics. Work along with me. Then download the sheets and practice, practice, practice. Watch the video as many times as you need to. How To Solve Linear Inequalities Now that you have learned to solve linear equations, let's take a look at inequalities. There are very few differences in solving linear inequalities and solving linear equations so this will be easy for you to understand with a little practice. Several examples are included on this video to show you step-by-step how to proceed. They are not intended to be difficult but to show you how they differ from equations. Watch me work the problems first, then go back and work them by yourself. Compare your answers to mine. Even though linear inequalities can get much longer and more complex than these examples, they are worked the same way. The better you become at solving linear equations, the better you will be with inequalities. Equations are, at all times, stating that two quantities are equal. Inequalities are stating that, given two quantities, they may be unequal...and if they are, the inequality sign will tell you which one is larger. If Inequality statements are brand new to you, they are first introduced on the Number Line video. Solving Linear Equations Once you have learned the basic of the language of Algebra you will quickly start solving equations. The first equations you will solve are linear equations. This video breaks down the process of solving linear equations into easy-to-follow steps. The equations on this video are all one step equations. The examples show you how to use the inverse operation to get the variable by itself. The goal is always to get the variable on a side by itself. As you move into any advanced math class you will always need to solve equations. This video is paced slowly to provide the first important steps for the foundation you will need. Stay tuned for more videos on solving equations. Work along with me and use all the downloadable practice. Solving Two Step Linear Equations When you first get started in Algebra, one of the first things you learn to do is solve equations. This video solves equations that require two steps. It shows you how to know which step to do first and how to check to see if your answer is correct. Equations in Algebra get to be much longer and 'more complicated' than these. This is where you start so that you will have the foundation to move ahead. If you are absent from school when your teacher explains this process, this video will help you 'catch up' quickly. Whew! That's a good feeling. Being lost and getting behind is no fun! Meaning Of Exponents Exponents are everywhere in Algebra. You just can't get very far without understanding what they are and how they work. When you watch this video you will learn exactly that. Exponents are wonderful shortcuts and they speak a language of their own. Always begin at the beginning, at the most basic level. You will have a good foundation that way and you will build your confidence in mathematics. Download the Guide and along with me as you watch the video. Pat yourself on the back every time you are correct. I know that will be most of the time. :) If it isn't, ask me to slow down or repeat something for you by stopping the video and replaying what you need to hear and see again. The download the Practice Sheet. Master these little, tiny numbers and they will never defeat you. Laws Of Exponents Once you really understand what exponents are, it's time to learn how to use them. Whenever you notice the same thing occuring over and over again in math, you can expect to find a law. Exponent Laws are derived from patterns that show up every time you use the meaning of exponents. When you multiply, patterns show up. When you divide, patterns show up. When you raise a power to another power, patterns show up. This video will explain each one of these patterns and show you exactly how they work. Then you will learn the Laws of Exponents. It is information you really need to practice until it becomes natural. Work the "Guide" as you watch the video. Then work the Practice page. Algebraic Examples In Geometry Sometimes you just need extra practice in solving geometry problems using algebra. Most students like this part of Geometry more than proofs and definitons. Do you? You have four problems to solve on this video. Work them along with me. One is vertical angles. One uses angle bisector. A third problem uses linear pairs and the last problem uses supplementary angles. First of all, solve for x. Then find the measure of the angle. It is so easy to double check these and know for sure if you are right. I think you'll like these. As I say in the videa "Math is not a spectator sport." You can't just watch and just listen if you want to really learn and remember what you learn. You have to do the problems too. Work them with me, then work them by yourself. Using Algebra To Find Angle Measures Did you like Algebra? I hope so, because, many times in Geometry you are asked to solve for x. So if you thought you could get away from Algebra, oops, you were wrong! If you liked Algebra you are probably cheering to get back where you are comfortable. You must also know your geometry definitions to know how to set up your algebra equation. Solving the equation is almost always easy...once it is set up. The hard part comes when you are trying to set it up! The more definitions (in Geometry) that you really understand, the easier it is to set up your equation. Watch me and you'll see what I mean. In this video I will work problems with angle bisectors that form angles with equal measures. Also we'll work with linear pairs and supplementary angles. Commutative, Associative, Distributive, Identity This video explains the Commutative, Associative, and Distributive Properties. They are not very fun or interesting,to tell you the truth, but you need to know them. When I first learned them I thought they were pointless. I didn't understand why in the world they were in every math course I took. You may be like that too. Eventually, as you take more and more math classes, you will see that they never go away...and you'll begin to understand why you need these properties. This video lesson is more like eating your veggies than eating dessert! Just telling you the truth. Supplementary Files: Once you purchase this series you will have access to these files: Guide_and_Practice_Combining_Like_Terms.pdf ANSWERS_Combining_Like_Terms.pdf Multiplying_In_Algebra_Guide.pdf Practice_Multiplying_In_Algebra.pdf ANSWER__How_To_Multiply_In_Algebra.pdf Practice_For_Number_Line_and_Integers.pdf ANSWERS_Number_Line_and_Integers.pdf Guide_Multiplication_Sign_Rules.pdf Practice_Multiplication_Sign_Rules.pdf ANSWERS_Mult_Signs_Rules.pdf Guide_Mult_With_Sign_Numbers_Cont.pdf Practice_Mult_With_Sign_Numbers_cont.pdf ANSWERS_Mult_of_Sign_Numbers_cont.pdf Guide_Positive_and_Negative_Numbers.pdf Practice_for_Adding_Postive_and_Negative_Numbers.pdf ANSWERS_Positive_and_Negative_Numbers.pdf Guide_Inequalities.pdf Practice_Solving_Inequalities.pdf ANSWERS_Solving_Inequalities.pdf Practice_for_Solving_One_Step_Linear_Equation.pdf Guide_Solving_Linear_Equations.pdf ANSWERS_One_Step_Equations.pdf Guide_and_Practice_2-Step_Equation.pdf ANSWERS_Two_Step_Linear_Equations.pdf Practice_Meaning_of_Exp.pdf Meaning_Of_Exponents_Guide.pdf ANSWERS_Meaning_of_Exp.pdf Laws_Of_Exponents_Guide.pdf Practice_Laws_Of_Exponents.pdf ANSWERS_Exp_Practice.pdf Buy Now and Start Learning Buy this series to watch it immediately. View it as many times as you need and download it to your computer or iPod (most lessons). Satisfaction's guaranteed, so go get started!
Tutoring Matters: Everything You Always Wanted to Know about How to Tutor 2nd EditionAutoCAD 2010 Tutor for Engineering Graphics is a classic reference work featuring self-paced tutorials that lead both students and engineering graphic professionals from simple one-view engineering drawings to geometric constructions, multiview projections, section and auxiliary views, 3D solid modeling, and photorealistic rendering. Tutorials utilize a step-by-step approach, following traditional engineering drawing techniques and methods while teaching users how to take full advantage of AutoCAD 2010 to achieve professional results. AC circuit analysis gives many students problems, but in reality any student can fully understand how to analyze circuits that involve Alternating Current. In this course, the student will first begin by understanding what Alternating Current is and why it is important. Next, well review essential math concepts such as complex numbers and sinusoidal functions. Next, we will introduce the important topic of the Phasor, which will be the primary tool that we will use to solve AC circuits with sinusoidal sources. Finally, we will learn about impedance and how to solve AC circuits using phasors that involve kirchhoffs laws, series/parallel combinations, and more. Every topic is taught with step-by-step solved example problems
Fundamentals of College algebra (10 classic in the series of highly respected Swokowski and Cole mathematics books, the Tenth Edition of FUNDAMENTALS OF COLLEGE ALGEBRA retains the elements that have made it so popular. Once again, the book provides a clear writing style, an appealing uncluttered layout, clear exposition, time-tested exercise sets that feature a variety of applications, and problems that are appropriate and consistent in level of difficulty. This book is clearly sets itself apart from the competition--it is mathematically sound, prepares students for further mathematics courses, and offers excellent problem sets. This new edition has been improved and all of the chapters now include numerous technology inserts with specific keystrokes for the TI-83 Plus and the TI-86 graphing calculators, which is very helpful to students who are working with a calculator for the first time.
Thinking and Quantitative Reasoning Designed for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need ...Show synopsisDesigned for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need to learn in order to be better quantitative thinkers and decision-makers. The author team's approach emphasizes collaborative learning and critical thinking while presenting problem solving in purposeful and meaningful contexts. While this text is more concise than the author team's Mathematical Excursions ((c) 2007), it contains many of the same features and learning techniques, such as the proven Aufmann Interactive Method. An extensive technology package provides instructors and students with a comprehensive set of support tool80618777389-4Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780618777389Very Good. In Very Good Condition! ! Copyright 2008ISBN:...Very Good. In Very Good Condition! ! Copyright 2008ISBN: 0618777385Houghton Mifflin; Instructor's Annotated Edition Mathematical thinking and Quantitative Reasoning [Hardcover] 724pgsSlight wear, binding is tight, all pages are intact. We ship daily Mon-Sat. We will not process or accept International Orders! These orders will be cancelled automatically! Thank you for your cooperation
Math 90 (20329) – Intermediate Algebra Spring 2011 Instructor: Barbara Nilson Office: 2762 Phone: 355-6477 E-mail: bnilson@imperial.edu or barbaranilson@gmail.com Text: Intermediate Algebra 10th ed., Lial, Hornsby, McGinnis – Chapters 1 – 10 Homework: MathXL (purchase can be made bookstore) Final: Saturday, June 4, 3:30pm – 6pm Or online with a credit card Drop: May 14, 2011 Pre- requisite: Math 80 –Beginning Algebra (grade of C or better) or appropriate placemen exam score Any student with a documented disability who may need educational accommodations should notify the instructor or the Disabled Student Programs and Services (DSPS) office as soon as possible. DSPS, Rm 2117, Health Science Building – 355-6312 Final  The common final for the Spring 2009 semester for all sections of Math 090 will be given on Saturday,June 4, 2011 from 4:00 – 6:00 p.m. at the IVC main campus. If you need to take the final exam at any other time than scheduled you need to complete and submit a Student Petition.  Rooms designated to take the common final are still to be determined.  Students should be at testing site at 3:30 p.m. with: 1. have picture ID 2. your G number 3. course section code (10393) and instructor's name 4. #2 pencil and erasers 5. calculator – No graphing calculators, cell phones, or other communication devices are allowed during the final. Course: Equivalent to a second year algebra offered in high school. Areas covered are the real number system, polynomials, rational expressions, exponential and radical forms, linear and quadratic equations, relations, functions and graphs, systems of equations and logarithmic and exponential functions. Chapters covered are selections from 1- 10. Student Learning Outcomes: Critical Thinking Upon successful completion of this course, students are expected to:  Understand the fundamental methods and strategies of problem solving by demonstrating the steps to multi- step problems  Demonstrate knowledge of mathematical facts and the use of these facts in problem solving and computation  Show the connectivity between concepts of linear equations and graphs  Demonstrate a knowledge of exponents and the connectivity to equations, graphs, and logarithmic forms th Homework: Homework is on MathXL for Intermediate Algebra, 10 ed, a supplement to your textbook. Instructions are at the end of this document. You can use the Math Lab or any internet connection once you have registered for the course. Your homework assignments are listed in the course and scores are stored there also. You can check at anytime to see what you have completed and what your score is. You can also use the practice quizzes and exams, watch a video, or ask for tutoring. Be aware of due dates as the homework sections will close after a given date. I will give you hands-on instruction in the Math Lab. Be sure to bring your access code if you do not check in on your own computer. Quizzes: We may be approximately 8 – 12 short quizzes, generally from that week's lecture and activities. They will be worth between 5 - 15 points. There is no makeup for quizzes. Exams: There will be 3-4 exams worth 100 points each. There is no makeup of exams. Final Exam: It will be comprehensive and a "common final" worth approximately 20% of your final grade. Attendance is expected. I may drop you after missing a total of 4 credit hours. Please contact me if you miss more than 2 classes and wish to remain enrolled. It is your obligation to drop if you do not want to receive a failing grade after May 14, 2011, the last day to withdraw from classes with a "W." Class Expectations:  Cell phones should be off during class.  Bottled water is the only food or drink allowed in the room.  Disruption of other students will result in a reprimand or expulsions from the class for that day. A second offense can result in administrative discipline.  Cheating is not tolerated and will result in discipline from the administration.  Quality work is expected. If a student meets the stated requirements for an assignment, but does it in a minimal fashion, the maximum grade for the product will be points valued at "C". To earn points valued at "B" or "A" there must be reasonable quality in the work. Grading: Standard scale - 90% = A, 80% = B, 70% = C, 60% = D, below 60% = F. Planned elements: (approximate percentage values for HW, quizzes, and exams) Homework 30% Quizzes 10% Final Grade = points earned Exams 40% points assigned Final 20% Possible difficulties with MathXL  Program tells you that your answer is incorrect when your answer actually matches – do not panic!! You can print that page and hand it in, or you can simply write a brief note in email that this problem has occurred and I will trust you.  Your home computer or internet is not functioning at the due date – Let me know and I will give you a grace period to turn it in. Be prepared for these kinds of emergencies and think about how you will solve the problem.  The math lab is not open at the time you are free – you can ask another computer lab on campus if you can download the necessary components of MathXL. Homework is listed on the left-side button in MathXL. Due dates are listed with the assignment. Keep up with the schedule because HW is a BIG part of you grade. Optional - Ma060 - Math Lab is 1 Math credit for a minimum of 36 hours in the lab during the semester. If you plan to do your HW in the lab or if you desire the 1 credit, this is a good choice. You will have tutors available to assist when you need help. Study guides, workshops, tutors, and videos are available. How to Register and Enroll in Your Course Welcome to MathXL! Your instructor has set up a MathXL course for you. The course name is: Sp2011 Math 90 It is based on this textbook: Lial: Intermediate Algebra, 10e To join this course, you need to register for MathXL and then enroll in the course. 1. Registering for MathXL Before you begin, make sure you have the access code that comes with your MathXL Access Kit. If you don't have an access kit, you can buy the code online by clicking Buy Now at To register, go to the for MathXL, click the Register button, and then follow the instructions on the screen. 2. Enrolling in your instructor's course After registering, log in to MathXL with your username and password. To enroll in this course, enter the following Course ID: The Course ID for your course is: XL0N-A1MA-201Y-99I2 (Clarification: X L zero N – A one M A – 2 zero one Y – 9 9 I(letter i) 2) Need more help? To view a complete set of instructions on registering and enrolling, go to and visit the Tours
Peer Review Ratings Overall Rating: Mathway is a mathematics problem solving tool where students can select their math and enter a problem. The computer solves the problem andbut only shows the steps for the solution if you have a paid subscription. It also has a worksheet generator and glossary. Learning Goals: To check the answers to mathematics problems and (with a paid subscription) review the steps in the solution. Target Student Population: Students in basic math, geometry, algebra, precalculus, calculus, and statistics. Prerequisite Knowledge or Skills: None. Type of Material: Drill and practice. Answer checking reference. Recommended Uses: Homework or test preparation resource. Technical Requirements: Any modern browser with JavaScript enabled. Evaluation and Observation Content Quality Rating: Strengths: The site allows the user to enter in just about any math problem from basic math, geometry, algebra, precalculus, calculus, statistics, finite math or linear algebra. There is a very large collection of problem types that this tool can solve. It quickly solves the problem and shows the answer. An instructor can also use the site to create a worksheet in a specified content area, with a specified number of questions. A glossary of hundreds of math terms is also on the site. Concerns: In order to use the full power of the site, the student must pay a substantial monthly subscription fee. With this fee, the student will not be distracted by advertisements and will be able to view the steps used to solve the equation. Without this fee all the student can see is the final answer, which severely limits any pedagogical use. This review is based on the free version which does have the distracting advertisements and does not show the steps. Potential Effectiveness as a Teaching Tool Rating: Strengths: The free site is not a teaching tool. A student who wants to check his or her answer can use this site to get the answer quickly. Concerns: Since the free version only shows the answer, a student using this version will not be able to learn the process used to solve the problem or get an explanation of any of the concepts. Ease of Use for Both Students and Faculty Rating: Strengths: There is an extensive list of examples that students can use as templates for the problems that they will be solving. Once the problem is entered there is a single button to solve the problem. There are clearly labeled tabs for solving, graphing, worksheets and the glossary. The mathematics engine appears to be very capable and quickly produces correct answers in a wide selection of mathematics
advances in dynamics, with wide applications throughout the sciences and engineering, have meant that a new approach to the subject is needed. Furthermore, the mathematical and scientific background of students has changed in recent years. In this book, the subject of dynamics is introduced at undergraduate level through the elementary qualitative theory of differential equations, the geometry of phrase curves and the theory of stability. Each subject, from the most elementary topic to some important discoveries of recent decades, is introduced through simple examples and illustrated with many diagrams. The text is supplemented with over a hundred exercises. The examples and exercises cover subjects as diverse as mechanics and population dynamics. The mathematical background required of the reader is an understanding of the elementary theory of differential equations and matrix arithmetic. The book will be of interest to second-year and third-year undergraduates at universities, polytechnics and technical colleges who are studying science and engineering courses. It is also suitable for graduates and research workers in such fields as plasma, atomic, particle and molecular physics, astronomy and theoretical ecology.
Mathematics for the Fundamentals of Engineering Examination Ace the math section of your PE exam. If you're preparing for the PE Exam, here's the help you need to pass the rigorous mathematics section of Part A on the very first try. In Mathematics for the Fundamentals-of-Engineering Examination, author Max Kurtz brings you his 35 years of experience training engineers for the PE exam. His easy-does-it approach helps you visualize complex mathematical principles and procedures to give you a solid grasp of their application in the engineering sciences. It also gives you tips for punching out correct calculations in record time using your trusty calculator. The outstanding preparation tool takes the sweat out of: algebra; set theory; matrix algebra; statistics and probability of discrete variables; differential calculus; plane geometry and trigonometry; plane and solid analytical geometry; properties of areas, volumes, and masses; integral calculus; statistics and probability of continuous printer. Repacking Your Bags helps people develop their own unique vision of the good life and take practical steps at home and at work to make that vision a reality. Repacking is a travel guide for success ... In this powerful, sometimes harrowing, deeply felt story, Patrick Tracey journeys to Ireland to track the origin and solve the mystery of his Irish-American family's multigenerational struggle with ...
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course AP Calculus AB B Course content General info Part of the Curriculum: Class information AP Calculus AB Part B is the second part of a full academic year of work in calculus and related topics, comparable to courses in colleges and universities. Students must have a thorough knowledge of college preparatory mathematics including algebra, axiomatic geometry, trigonometry, and analytic geometry. Topics include: Functions, Graphs, Limits, Derivatives and Integrals. Conceptual understanding of the essential concepts of calculus is emphasized in theory and practice. Professional mathematics organizations have strongly endorsed the use of graphing calculators in mathematics instruction, and consequently these calculators are also used throughout the course and required for a portion of the AP exam. Due to the rigorous nature of this course, students who are considering taking AP Calculus should seek the advice of their current mathematics teacher.
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In... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof." Charles Ashbacher, Journal of Recreational Mathematics Book Description Looking for a head start in your undergraduate degree in mathematics? This friendly companion eases beginning students into real mathematical thinking, unlocking important techniques for effective mathematics so you can communicate with clarity, solve problems, and explore the world of definitions, theorems and proofs with real confidence. About the Author Kevin Houston is Senior Lecturer in Mathematics at the University of Leeds.
+ By spelslottet.se Get Graphoid - the graphing scientific calculator with fast and easy zoom. Use the scientific calculator look-alike touch keyboard to enter expressions and functions, all on one screen without "2nd" key. Draw graphs or value tables, zoom in the values of the value table or graph by just touching the screen. Calculate min, max, intersections and more in graph mode as well as in table mode! * EASY TO ZOOM GRAPHS OF FUNCTIONS Use pinch zoom (two-finger zoom) to zoom graphs on multitouch devices. On older devices you can use one-finger zoom. Just long press the graphs to enter the zoom mode. Then just drag left/right/up/down to zoom. The scale grid is automatically updated. To select the interesting parts of the graphs has never been easier! With Graphoid calculator you can focus on inspecting graphs of functions, not how to use menus. * ZOOMABLE VALUE TABLE OF FUNCTIONS The functions can be investigated by a value table as well. By dragging the table up/down you move the visible interval of the function. You can even zoom the table values with pinch zoom on multitouch devices or by using the zoom buttons on the screen on non-multitouch devices. The differences between the x-values are auto calculated to be human readable. Rotate the device to portrait format and compare two functions in the table. Of course you can calculate min, max, intersections etc right from the table screen. To inspect functions with a value table is faster, easier and more intuitive than ever with Graphoid! * SYNTAX HIGHLIGHTING INCREASES READABILITY When you enter expressions or functions they are displayed with colored text; the negative sign has a different color than the subtraction sign, the scientific notation 'E' is highlighted by color so you don't miss it (we all have received answers like 1.394735386937635E9 without notice the 'E'). During the input of an expression matching parentheses are highlighted with color to make multi parentheses input more readable. * EASY HUMAN READABLE ERROR MESSAGES In case you enter an illegal expression you will get an easy-to-read error message. Also, if a calculation error occur a specific human-friendly error message will tell you what went wrong; 'Division by zero', 'Log of a negative number is illegal' etc. Graphoid is made to help us avoid mistakes! * STORED VARIABLES AND EXPRESSIONS You can easily store variables with an arbitrary name and use them in future calculations. The last entered expressions are automatically stored and can be reused or edited.
apply the concept of the integral in order to calculate the volume of an object. Students will work on problems that involve a function which revolves around the x-axis to make a three dimensional shape, with the goal being to find the volume of the shape. Grades 9-12
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Calc-Add A calculator and adding machine with many features including: the ability to stay on top; commas in the entry box; Micro Window; toggle between two window sizes; Tape Display (history), saving, printing and annotating; and a Stationary Decimal. Matho-Sub The objective of this software is to improve Mental Subtraction. After a regular practice on Subtraction software your kid's calculation speed should increase 10 to 15 times. MATHO-Sub software has been divided in three levels viz. Functions_2 Functions_2 program discusses functions in more depth. It includes relations and their graphs, discuss a function from different aspects including how to determine a graph is a functional graph or not. What is ordered pairs. Simple Tools Simple Tools is an extremely simple to use tool that calculates areas and volumes. STFMath STFMath is a multipurpose math utility, suitable not only for students, but also for engineers, professors, or anyone interested in math: functions (draw, analyze, evaluate), calculators (complex, matrix, geometry, scientific) and more.
Algebra Concepts And Applications, Noteables 9780078729850 ISBN: 0078729858 Publisher: McGraw-Hill Higher Education Summary: NoteablesTM: Interactive Study Notebook with FoldablesTM is a complete note-taking system with guided note taking for every lesson - in a workbook format. Plus, vocabulary builder and a chapter test preparation section are included for every chapter. Zike, Dinah is the author of Algebra Concepts And Applications, Noteables, published under ISBN 9780078729850 and 0078729858. Two hundred nine Algebra Concepts ...And Applications, Noteables textbooks are available for sale on ValoreBooks.com, one hundred eight used from the cheapest price of $5.24, or buy new starting at $19.07.[read more]
Interactivate Impossible Graphs Abstract This lesson is devoted to impossible graphs. Users of the module can learn to distinguish between possible and impossible graphs of functions, and to learn why some graphs are impossible. These activities together give a brief lesson that can be completed in as little as 30 minutes class-time, depending on how many teams need to share their ideas. The discovery process takes about 15 minutes, and each presentation about 5 minutes. Objectives Upon completion of this lesson, students will: have practiced plotting functions on the Cartesian coordinate plane be able to read a graph, answering questions about the situation described by the graph be able to look at a graph and decide if it makes sense Standards Addressed: Grade 10 Functions and Relationships The student demonstrates conceptual understanding of functions, patterns, or sequences including those represented in real-world situations. The student demonstrates algebraic thinking. Grade 9 Functions and Relationships The student demonstrates conceptual understanding of functions, patterns, or sequences including those represented in real-world situations. The student demonstrates algebraic thinking. Functions Interpreting Functions Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Analyze functions using different representations Linear, Quadratic, and Exponential Models Interpret expressions for functions in terms of the situation they model Grades 9-12 Algebra Represent and analyze mathematical situations and structures using algebraic symbols Understand patterns, relations, and functions Algebra 1 Algebra Competency Goal 4: The learner will use relations and functions to solve problems. Algebra I Algebra Competency Goal 4: The learner will use relations and functions to solve problems. Grade 8 Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra COMPETENCY GOAL 5: The learner will understand and use linear relations and functions. Introductory Mathematics Algebra COMPETENCY GOAL 4: The learner will understand and use linear relations and functions. COMPETENCY GOAL 5: The learner will understand and use linear relations and functions. 8th grade Geometry The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane. The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation Elementary Algebra Elementary Algebra Standard EA-3: The student will demonstrate through the mathematical processes an understanding of relationships and functions. Intermediate Algebra Algebra The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Secondary Algebra II AII.12 The student will represent problem situations with a system of linear equations and solve the system, using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations. AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions. Next have a "live" discussion while going through the Possible or not? Activity . Give each group of students a different graph from the database, and have them present their ideas and findings to the entire class. Independent Practice If you choose to pass out the impossible graphs worksheet have the students work independantly or in small groups to complete it. Closure You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson. Alternate Outline This lesson can be rearranged in several ways. This lesson can be extended to include not only impossible graphs, but also non-function graphs (those that do not pass the vertical line test). This lesson can be extended to include having each team of students discuss a situation in which the impossible graph could be possible. This is a good place to discuss how time is not the only possible independent variable. Suggested Follow-Up After these discussions and activities, students will have more experience with functions and relationship between the English description, graphical and algebraic representations - including what cannot occur.
The course Algebra 1 is part of the 16 online courses in MUST high school home study diploma program. It covers extensive subject knowledge and the course contents enrich the students' learning. It covers online study material that is free of cost for students at MUST. This online course of the home school diploma program is ahead of all other traditional & online courses. This course can be accessed in the MUST High School's online Classroom which covers both theory and practical aspects of the courses and includes case studies and real-life examples. Our online high school classes are very flexible. There is no fixed time for the high school classes online. You may enter into your online classroom 24x7 and can study according to your pace. So whether you are a student interested in online homeschooling diploma or a working adult interested in getting high school diploma from home or office, you may study English 9 course online with complete ease. To see why MUST's homeschool / online high school diploma is the first choice of working adults and homeschool students across the globe, please Click here. Topics Covered in This Course: Section 1 Expressions, Equations, And Functions Overview: An expression is a syntactic concept of the variables of relevance. Equations are used to state the equality of two expressions containing one or more variables. A function expresses dependence between two quantities. This topic elaborates on that. Properties Of Real Numbers Overview: The real numbers may be described informally as numbers with an infinite decimal representation. The real numbers include the rational numbers and the irrational numbers. This topic elaborates on that. Section 2 Solving Linear Equations Overview: This section's topic 1 teaches you the theory of linear equation - an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one, two, three or more variables. Graphing Linear Equations And Functions Overview: This section's topic 2 teaches you the theory of slope - used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. Overview: Polynomials are one of the most important concepts in algebra and throughout mathematics and science. Factoring is the decomposition of an object into a product of other objects. This topic elaborates on that. Quadratic Equations And Functions Overview: A quadratic equation is a polynomial equation of the second degree and a quadratic function is a polynomial function. This topic elaborates on that. High School Diploma Program High school diploma program offered by MUST High School surpasses the similar traditional programs offered by world-class high schools across the globe in terms of ease & flexibility, affordability, quickness and quality of education. To read more about why MUST High School is the first choice of working adults and students across the globe, please Click here You can get credits for your prior learning. If you have strong command in some courses (through your work experience, prior knowledge or trainings, etc.) you can get their credits! So you won't have to study that course and both your tuition and time required will be reduced. Read more Credit Transfer If you have already studied some courses of high school diploma and have its transcript, we will accept the credit hours of those courses and reduce the equivalent from your program. So you won't have to study that course again. This will reduce both your tuition and time required to complete your education. Read more
ALEX Lesson Plans Title: Know Your Limits Description: TheStandard(s): [MA2010] PRE (9-12) 4: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. (Alabama) Subject: Mathematics (9 - 12) Title: Know Your Limits Description: The Thinkfinity Lesson Plans Title: Conduct an Experiment [MA2010] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) Subject: Mathematics,Science Title: Conduct an Experiment Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Whelk-Come to Mathematics Description: In Standard(s): specific AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) Subject: Mathematics,Science Title: Whelk-Come to MathematicsTitle: Northwestern Crows Subject: Mathematics,Science Title: Northwestern Crows Thinkfinity Learning Activities Title: Limits Description: This student interactive, from an Illuminations lesson, allows students to see a representation of three geometric series and the harmonic series. Standard(s): [MA2010] DM1 (9-12) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) [MA2010] PRE (9-12) 4: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. (Alabama) [MA2010] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) Subject: Mathematics Title: Limits Description: This student interactive, from an Illuminations lesson, allows students to see a representation of three geometric series and the harmonic series. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Ng is very polite but he rushes explanations and his notes don't distinguish scalars/vectors/matrices. He overloads the meaning of various notational terms. Homework is very hard (most TAs don't understand it) and requires you to know magic never taught in class. Great subject but absolutely ridiculous course. Professional Ng is an amazing lecturer, absolutely top notch. His notes are extremely detailed and refined. But going to his class is still a plus, he's clear, to the point and extremely good with giving examples for anything that might be fuzzy in the notes. The class is not easy however - at least for me, the homework really requires a lot work. Absolutely amazing! Genuinely interested in the subject, explains concepts with clarity, uses excellent examples and focuses on what's important. Usually you'd need to meet a professor in person to iron out problems and understanding. He managed to teach via lecture videos and STILL got through to most people. Absolutely amazing! A great teacher who always explains hard-to-understand concept in a easy way. The programming exercises really helps me gain deeper understanding about ML. The course is hard, but Prof really really did a good job! His lecture notes are very clear, but he's a terrible lecturer in person. He mumbles and writes equations on the board without differentiating useful ones from algebraic derivations. I'm very serious when I say that he draws arrows labeled "magic" when he gets tired of explaining things.
Let MOM help you with your math Progress in upgrading math's tools has been uneven: blackboards have become whiteboards, but calculators and software have come up short in trying to replicate the speed and simplicity of pencil and paper. Math-o-mir is the result of the surprisingly difficult effort to develop a software-based equation editor to meet that need. It's a free tool with one goal, to make writing and editing mathematical equations as easy and natural as scribbling on a pad. It's not a math engine, design tool, or image editor, though it uses some of the same concepts, such as freehand drawing and the ability to insert expressions and expression elements into equations with a few clicks. Math-o-mir's simple interface resembles many graphics editors, only its tools palette contains mathematical symbols instead of the typical brushes and color pickers. The blank main field includes an optional pegboard background, and the interface can be customized in various ways, such as font size and halftone rendering. Math-o-mir (or MOM for short) won't be difficult for the average math whiz to figure out, but those of us whose times-and-gozintas are a little rusty will want to download and examine the extensive PDF-based user manual. For example, we wouldn't have known to check Options/Keyboards to see if general variable mode, simple variable mode, or very simple variable mode was selected. The manual does a great job of starting users off by showing how to write Einstein's famous equation, E=MC2. We expanded the hand-drawing tools on the palette, which let us draw lines and vectors and insert a variety of basic shapes as well as objects such as question marks and checkmarks. We could copy and save equation images, copy MathML code, and access a virtual keyboard, too. Math-o-mir is a unique program, and uniquely useful to people who need to scribble down equations, like teachers, students, engineers, and businesspeople
Elementary Algebra : Graphs and Models - 05 edition Summary: Geared toward helping students visualize and apply mathematics, Elementary Algebra: Graphs and Models uses illustrations, graphs, and graphing technology to enhance students' mathematical skills. This is accomplished through Interactive Discoveries, Algebraic/Graphical Side-by-Sides, and the incorporation of real-data applications. In addition, students are taught problem-solving skills using the Bittinger hallmark five-step problem-solving process coupled with Connec...show moreting the Concepts and Aha! exercises. And, as you have come to expect with any Bittinger text, we bring you a complete supplements package that now includes an Annotated Instructor's Edition and MyMathLab, Addison-Wesley's online course solution
To encourage students to actively involve in participative learning of English and to help them ... You Can Win by Shiv Khera - Macmillan Publishers India ... mathematics courses offered for Engineers and Scientists. ..... 4. BehrouzForouzan and Firouz Mosharraf – "Basics of Computer Science"-CengageLearning 2009
CBSE board Exams 2009 begin in a few days from now on 2 march 2009. Mathematics paper is on 14 March 2009. Students have upto 10 days for preparing this paper depending on their subjects. This year too we bring for you latest pre exam tips by experienced CBSE school teachers. In the last years sudents have beniffited a lot with our tips. As usual we begin with students who find mathematics very difficult. These students should begin with some selected topics which are comparitively easy to ensure that they pass in the exams. 1. Number System - 4 marks. Most of the questions are very easy. Students should read theorems (see here)Methods to find HCF, LCM etc. Sample paper of this chapter is available here 2. Number System 3 - 4 marks. This is another easy chapter . Learn imporant formulae (see here). Questions include forming polynomials when zeros are given or when sum and product of zeros are given. Solve sample paper from this chapter here 3. Graph - 3 marks(from linear equations in 2 var.) see important formulae here The second topic is graph from the chapter of linear equations in two variables in which we solve 1, 2 or 3 equations graphically. Solve sample paper from this chapter.Get it. 4. Theorems - 6 marks (with one small question) Theorems from the two chapters of Triangles and Circles are about 7 in number and can be easily done. 5.Constructions - 3 marks Do not forget this small chapter.Solve sample paper here. 6. Statistics - 10 marks (inclusive of probability) In this chpater atudents calculate mean (3 methods), mode or median from given table. We also need to know method to change frequency table to less than or more than C.F. tables and vice versa. Ogive (less than or more than type) are drawn on graph and median may calculated from it. Solve sample paper from this chapter.Get it We also need to study probability. Get sample paper for this chapter. click here Every possible care has been taken to prepare sample papers and to put up other information. cbsemath.com is not responsible for typing and other errors that may creep in. cbsemath.com will also not be responsible for any deviations from our views in the actual paper.
About: Factoring Polynomials: Factoring a Monomial from a Polynomial Metadata Name: Factoring Polynomials: Factoring a Monomial from a Polynomial ID: m21906 Language: English (en) Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses. The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. Objectives of this module: be able to factor a monomial from a polynomial.
Developing a Clear Learning Target About This Topic Thread Algebra is best learned as a set of concepts and techniques tied to the representation of quantitative relations and as a style of mathematical thinking for formalizing patterns, functions, and generalizations. Although many adults think that algebra is an area of mathematics more suited to middle school or high school students, even young children can be encouraged to use algebraic reasoning as they study numbers and operations and as they investigate patterns and relations among sets of numbers. In the Algebra Standard, the connections of algebra to number and everyday situations are extended in the later grade bands to include geometric ideas. Explore the effect of transformations on geometric figures and shapes in the coordinate plane. Scaffolded (Unpacked) Ideas Students should be able to understand the relationships among tables, graphs, and symbols and to judge the advantages and disadvantages of each way of representing relationships for particular purposes. Systematic experience with patterns can build up to an understanding of the idea of function. Students can study sequences that can best be defined and computed using recursion, such as the Fibonacci sequence, 1, 1, 2, 3, 5, 8, .... Recursive sequences appear naturally in many contexts and can be studied using technology. Students should be able to understand the relationships among tables, graphs, and symbols and to judge the advantages and disadvantages of each way of representing relationships for particular purposes.
contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: - fully worked-out examples; - many carefully selected and formulated problems; - fast Fourier transform methods; - a thorough discussion of some important minimization methods; - solution of stiff or implicit ordinary differential equations and of differential algebraic systems; - modern shooting techniques for solving two-point boundary-value problems; - basics of multigrid methods. Included are numerous references to contemporary research literature.
The Kumon Math Curriculum Math Level G: Positive/Negative Numbers, Introduction to Algebra Students are introduced to positive and negative numbers, as well as to basic algebra. Students use their previously learned four operations skills to master linear equations. A word problem set rounds off the level, allowing students to apply everything they have learned in Level G. Math Level H: Linear Equations, Inequalities & Graphing Students will learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs
Summary: This text is for a one-term course in intermediate algebra, for students who have had a previous elementary algebra course. A five- step problem-solving process is introduced, and interesting applications are used to motivate students. Coverage progresses from graphs, functions, and linear equations to sequences, series, and the binomial theorem. New to this edition are sections on connecting concepts, study tips, and exercises designed to foster intuitive problem so...show morelving. Bittinger teaches at Indiana University; Ellenbogen at Community College of Vermont
Summary The new edition of BEGINNING ALGEBRA is an exciting and innovative revision that takes an already successful book and makes it more compelling for today's users. The new edition has been thoroughly updated with a new interior design and other pedagogical features that make the book both easier to read and easier to use. Known for its clear writing and an engaging, accessible approach that makes algebra relevant, BEGINNING ALGEBRA helps users to develop problem-solving skills and strategies that they can use in their everyday lives. The new edition welcomes two new co-authors Rosemary Karr and Marilyn Massey who along with David Gustafson have developed a learning plan to help users succeed in Beginning Algebra and transition to the next level in their coursework. Table of Contents Real Numbers and Their Basic Properties Real Numbers and Their Graphs Fractions Exponents and Order of Operations Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers Algebraic Expressions Properties of Real Numbers Projects Chapter Review Test Equations and Inequalities Solving Basic Linear Equations in One Variable Solving More Linear Equations in One Variable Simplifying Expressions to Solve Linear Equations in One Variable Formulas Introduction to Problem Solving Motion and Mixture Problems Solving Linear Inequalities in One Variable Projects Chapter Review Test Cumulative Review Exercises Graphing Writing Equations of Lines Functions Variation The Rectangular Coordinate System Graphing Linear Equations Slope of a Line Point-Slope Form Slope-Intercept Form Functions Variation Projects Chapter Review Test Polynomials Natural-Number Exponents Zero and Negative-Integer Exponents Scientific Notation Polynomials Adding and Subtracting Polynomials Multiplying Polynomials Dividing Polynomials by Monomials Dividing Polynomials by Polynomials Projects Chapter Review Test Cumulative Review Exercises Factoring Polynomials Factoring Out the Greatest Common Factor Factoring by Grouping Factoring the Difference of Two Squares Factoring Trinomials with a Leading Coefficient of Factoring General Trinomials Factoring the Sum and Difference of Two Cubes Summary of Factoring Techniques Solving Equations by Factoring Problem Solving Projects Chapter Review Test Rational Expressions And Equations Ratio and Proportion Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions Simplifying Complex Fractions Solving Equations That Contain Rational Expressions Solving Applications of Equations That Contain Rational Expressions Ratios Proportions and Similar Triangles Projects Chapter Review Test Cumulative Review Exercises Systems of Linear Equations and Inequalities Solving Systems of Linear Equations by Graphing Solving Systems of Linear Equations by Substitution Solving Systems of Linear Equations by Elimination (Addition) Applications of Systems of Equations Solving Systems of Linear Inequalities Projects Chapter Review Test Roots and Radical Expressions Square Roots and the Pythagorean Theorem. nth Roots and Radicands That Contain Variables
More About This Textbook Overview What is missing in most curricula - from elementary school all the way through to university education - is coursework focused on the development of problem-solving skills. Most students never learn how to think about solving problems. Besides being a lot of fun, a puzzle-based learning approach also does a remarkable job of convincing students that (a) science is useful and interesting, (b) the basic courses they take are relevant, (c) mathematics is not that scary (no need to hate it!), and (d) it is worthwhile to stay in school, get a degree, and move into the real world which is loaded with interesting problems (problems perceived as real-world puzzles
With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!. For more information about the title Calculus: Early Transcendentals (Stewart's Calculus SeriesMath Goes Viral in the Classroom(December 11, 2009) — At least a dozen Alberta high-school calculus classrooms were exposed to the West Nile virus recently. Luckily, it wasn't literally the illness. Educators used the virus as a theoretical tool when ... > read moreSoap Films Help to Solve Mathematical Problems(January 27, 2011) — Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors who have ... > read more
...Conic sections is also a familiar area of expertise. As an additional resource I also possess an Algebra II "Teacher's Edition" text. Word problems are a particular challenge for a number of students for whom the following steps must first be modeled: 1) drawing an appropriate diagram, if requ...
books.google.com - A... Introduction to Knot Theory An Introduction to Knot Theory A and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area. An Introduction to the Theory of Knots Although beyond the scope of this leisurely introduction to knot theory, one. of the most successfull and interesting ways to tell knots apart is through ... www-graphics.stanford.edu/ courses/ cs468-02-fall/ projects/ desanti.pdf
Fundamentals of Matrix Computations, 2e Written for advanced undergraduate students, graduate students, and professionals, this book provides a detailed explanation of matrix computations and the accompanying theory. Topics covered include the introduction of new methods for solving large, sparse eigenvalue problems, including the implicitly-restarted Arnoldi and Jacobi-Davidson methods; iterative methods; modern componentwise error analysis; reorthogonalization; and rank-one updates of the QR decomposition. Numerous example problems throughout the book are solved using MATLAB. Free Mathematical Modeling Technical Kit Learn how you can quickly build accurate mathematical models based on data or scientific principles.
MESA Helps Build Your Future! We help individuals achieve their academic goals. MESA CCCP (Math Engineering Science Achievement California Community College Program) provides support to community college students who are majoring in math, engineering and science so they can excel academically and transfer to four-year institutions. This course proceeds at an intense pace. Topics include: functions and graphs, applications of functions, exponential and logarithmic functions, trigonometric functions and analytic trigonometry, right triangle trigonometry, analytic geometry, and roots of polynomial equations. This course is intended for students planning to take calculus. Math 75 Mondays and Wednesdays 1:00-2:00pm, JM 122 Tuesdays and Thursdays 3:00-4:00pm, JM 124 This is the first course of a three-semester sequence. Topics include limits, continuity, differentiation, and integration involving many types of function with a variety of applications. Primarily for mathematics, physical science, and engineering majors. Math 76 Tuesdays and Thursdays 11:00am-12:00pm, JM 222 This is the second course of a three-semester sequence. Topics include techniques of integration, improper integrals, infinite series, analytic geometry, polar coordinates and parametric equations, vectors, three-dimensional space, and many applications. Math 77 Tuesdays and Wednesdays 2:00-3:00pm, JM 207 Math 80 Tuesdays and Fridays 2:00-4:00pm, JM 124 MATH080 Introduction to linear algebra including systems of linear equations, vectors, matrices and determinants, two and three-dimensional vectors, vector spaces, inner product spaces, eigenvalues and eigenvectors, and linear transformations. Intended for mathematics, engineering, or computer science majors. Supplemental learning assistance is available for students to strengthen skills and to reinforce student mastery of concepts. Students enrolled in MATH 80 may access the supplemental learning assistance by enrolling in MATH 400, an open entry/open exit non-credit course. Approved for Distance Learning format. Physics 6 Tuesdays and Thursdays 10:00am-12:00pm, JM 124 Physics 20 Mondays 11:00-12:00pm, JM 119 Wednesdays 1:00-2:30pm, JM 119 Chem 20 Mondays and Wednesdays 8:00-9:00am, JM 124 Wednesdays and Thursdays 4:00-5:00pm, JM 119 CHEM 20 is a one semester transferable college chemistry course designed to meet the needs of allied-health majors. The course is a study of the fundamental theories and laws of chemistry. The laboratory portion of the course involves experimentation and drawing conclusions from data. Chem 1 Tuesdays 2:00-4:00pm, JM 223 Fridays 2:00-4:00pm, JM 223 A course for majors and pre-professionals involving the fundamental theories and laws of chemistry. Topics include stoichiometery, atomic structure, bonding theories, ionic reactions and properties of gases.
Introduction to visual, step-by-step approach to solving engineering problems with Excel. Specifically targeted at first-year engineering students, this text seeks to teach the basic Excel skills that undergraduates will use in the first few years of engineering courses. This book was written with the understanding that students get frustrated by multi-step procedures that illustrate only the final outcome. Ron Larsen, in his hallmark approach, provides screen images for each and every each step allowing students to easily follow along as they try to ... MOREperform each task.
stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter. "The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal . . . Every library should have several copies" — Choice. 1976 edition.
Get latest information on Savings & Coupons for products like this and sign up our newsletter (*See our privacy policy): Features This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
learn equation search results We have developed the educational program "Linear Equations", not to replace the math teacher at high ... the software, and in the meantime they will learn in a unique way to resolve linear equations, which is an important part of mathematics. Linear equations are equations involving only one variable, like x or y, ... ... their cost. The program is very easy to learn - you don't need to read long manuals ... from table data or from the manually entered equations. You can specify the unlimited number of equations and tables and their graphs will be plotted ... Get into the pilot seat and learn about volume and surface area while blasting away ... game that offers an engaging environment for serious learning about geometric figures. As obstacles hurtle toward them, ... surface area. Galactic Geometry encourages true understanding of equations and provides arithmetic and mental math practice. With five curve fitting. Fit thousands of data into your equations in seconds: Curvefitter gives scientists, researchers and engineers ... model for even the most complex data, including equations that might never have been considered. You can build equation set which can include a wide array of ... data fitting includes the following capabilities: *Any user-defined equations of up to nine parameters and eight variables. ... ... Math (30sec & 60sec Modes) Solve as many equations as possible with the time limit. Points are awarded for solving each equation, and deducted for a wrong answer. You can choose to play for either 30 or 60 seconds at a time. Easy / Advanced / in BASIC or C to utilize any solved equation in a program that you have written. Macro ... ... flexible system for solving all the partial differential equation problems that come up in science and engineering, so you didn't have to buy and learn a new software tool for each problem? Well, ... FlexPDE is a scripted finite element partial differential equations problem solving environment. FlexPDE reads your partial differential equation system and problem domain definition in a natural, ... ... tools, and rich pre-drawn library templates. Easy to Learn, Easy to Use. Drawing does not need to ... Programs. With one-click buttons to import word, excel, equation files. Insert your CuteDraw charts into other document in just minutes. XML file format. Save Common graphic format support and printing what your see ...
Limits and Continuity Teacher Resources Find Limits and Continuity educational ideas and activities Title Resource Type Views Grade Rating In this limits and continuity test, students solve 8 multiple choice questions. They define the words limits and continuity. Students determine the limits of 8 functions. Students find the value for a constant in one function, and prove one function is continuous at x=0. 4 questions require students to graph functions. There are 25 questions in all (plus one extra credit question). Students investigate limits and continuity of functions. In this limits and continuity of functions lesson, students find the limit as a function approaches a given value. Students find the domain of functions. In this calculus activity, students work problems containing functions, limits and dealing with continuity. They evaluate functions and use the limits theorem to help find the correct answer. There are 26 questions. Twelfth graders investigate limits. In this Calculus lesson plan, 12th graders use the Ti-89 calculator to explore limits. Students examine the tables and graphs to approach limits from a numerical point of view. In this calculus activity, students complete a chart of values using limits and continuity. They use the test of continuity to solve most of the problems and match their answers to the correct answers. There are 18 matching questions with an answer key. read a description of how to evaluate limits then solve problems both with and without their graphing calculators. In this evaluating limits lesson, students evaluate 9 limits problems without their graphing calculators. Answers are checked using the calculator. Twelfth graders examine limits. In this Calculus activity students use the symbolic capacity of the TI-89 calculator to explore limits. Students examine the tables and graphs and use the information to support their answers.
Next: Linear Systems by Graphing Previous: Chapter 6 Test Chapter 7: Systems of Equations and Inequalities; Counting Methods Chapter Outline Loading Contents Chapter Summary Image Attributions Description This chapter introduces students to linear systems of equations and inequalities as well as probability and combinations. Operations on linear systems are covered, including addition, subtraction, multiplication, and division.
Line Integral - Green's Theorem This is a short introduction to Green's Theorem which concerns turning a closed loop integral into a double integral given certain conditions. Author(s): No creator set License information Related content No related items provided in this feed Autism This module opens with statistics and a description of autism and how the disorder has been viewed historically. Studies now support the theory that autism results from a lack of normal neural growth during prenatal development. Dr. Temple Grandin of Colorado State University, severely autistic as a child, is presented as someone who overcame her autism and managed to us Author(s): No creator set License information Related content No related items provided in this feed Introduction to Two Finger Math - Multiplication Strategy Part 1 of 2 Introduction to Jakow Trachtenberg's math method called the Two Finger Method (2FM). This strategy helps to gain control over numbers and also boosts concentration and memory. The instructor show the 4 rules of 2FM. Slide show with insert movie of the presenter. Interesting strategy. (10:00) Author(s): No creator set License information Related content No related items provided in this feed Intro to Algebra, Part 1 This clip provides a quick introduction to algebra. A couple of examples are shown on a white board to help students see the idea of how variables and reduction of equations can be useful. Author(s): No creator set License information Related content No related items provided in this feed Intro to Algebra, Part 6 This video introduces expansion of binomial factors, factoring expressions, and factoring through grouping (all part of an introduction to algebra). An instructor shows some examples on a whiteboard. Author(s): No creator set License information Related content No related items provided in this feedKey skills assessment unit: Application of number Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be applied in particular situations. Developing your numerical, graphical and algebraic skills means being able to plan how you are going to use your skills over a period of time, monitoring your progress and then reviewing your approach. In developing and assessalexander fleming This is an animated documentary about the life of alexander fleming and how he discovered penicillin. The short video only BRIEFLY covers Fleming's life, spending only a moment on the discovery of penicillin, but would be a nice introduction. The narrator speaks rather quickly but I found the animated cartoons to be oddly entertaining. (1:32) Author(s): No creator set How to Write A Five Paragraph Essay This slide show on how to write the common 5 paragraph essay has no voice narration. Text instructions are shown for the essay blueprint and explanations on introduction, thesis statement, body paragraphs, supporting details, and conclusion. MUSC Weight Management Center- Focus Program Focus is a 15-week weight loss program that combines both dietary supplements and a calorie controlled diet. Dietitian Laura Nance of the MUSC Weight Management Center explains more about the program. Author(s): No creator set License information Related content No related items provided in this feed Countable and Uncountable Nouns - part 4 Thisfourth and last part of the introduction to Nouns covers the topic of countable and uncountable nouns. Groups are shown of countable and uncountable nouns. Author(s): No creator set License information Related content No related items provided in this feed Word Parts-Alpha Wheel -Part 1 Introduction to English words, word parts (prefix, root, suffix) and words beginning with UN and ending with ABLE. The alpha wheel is a circle with letters around it that all words in the English language are built on. Words Author(s): No creator set License information Related content No related items provided in this feed The Pythagorean Theorem, Part 1 of 3 Thisfull screen' to see all the information more clearly. (10:46)The People's Party - Late 1800s This video is accompanied by text."The future looked bright for American farmers during the mid-1800s. But increased competition from farmers in other countries, including Canada, Russia, and Australia, sent American crop prices spiraling downward. By the 1890s, wheat sold for 60 cents a bushel, and the price for a pound of cotton fell below 6 cents. The quickly expanding railroad industry also played a part in breaking the spirit—and bank account—of the American farmer. Fierce Author(s): No creator set License information Related content No related items provided in this feed Growing Up in the Great Depression Quick overview of the difficulties people encountered during the Great Depression. A man tells his family's story of survival by stealing and moving from place to place. Would be a good introduction to the topic of the Great Depression and a possible essay prompt for students.
Elementary Statistics - With CD - 6th edition Summary: Elementary Statistics is appropriate for a one-semester introductory statistics course, with an algebra prerequisite. ES has a reputation for being thorough and precise, and for using real data extensively. Students find the book readable and clear, and the math level is right for the diverse population that takes the introductory statistics course. The text thoroughly explains and illustrates concepts through an abundance of worked out examples201771306
Discrete Mathematics not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper level mathematics courses.
clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Chapter 7, Geometry, has been extensively revised and re-organized to include a new section 7.1 on angles and new section 7.4 devoted to triangles. Increased coverage of estimating with fractions and decimals with new "To Think About" exercises in Sections 2.5, 2.8, and 3.3 and a new lesson in Section 3.7. Coverage of fractions in Chapter 2 has been expanded as follows: Section 2.6 now begins with a discussion of least common multiples so that the subsequent coverage of least common denominators is more complete; a new lesson on order of operations in Section 2.8 offers readers additional review of these rules and practice applying them to fractions; and a new mid-chapter test on fractions appears after Section 2.5. Percent applications are now covered in two sections (Sections 5.4 and 5.5) to allow for a more patient presentation of this important topic.
Distance Learning Class Critical Information MAT-160-N3/N4 College Algebra To Math 160 Online Students: This course is not easier than a lecture course. The course is not self-paced and late work will not be accepted. This course requires a very regimented and structured schedule. You will have assignments due regularly. The objectives for MAT 160-N3/N4 are the same as the on-campus College Algebra sections. Online students should plan to spend a minimum of 16-20 hours weekly working on course requirements. You should plan on visiting campus frequently to get help. If you are a very disciplined and self-motivated student, please read more. An online course provides students with a great deal of flexibility but there is an added level of difficulty and responsibility when learning math online. You need to consider this before starting a course of this type. Please click on the link below and take the quiz to learn about how well you are suited for online education. The Orientation for MAT 160-N3/N4 is online and will be posted on Moodle by Aug. 16, 2013. This Orientation must be completed before accessing the course. ALEKS ( is the electronic platform for this course. You will be responsible for signing up and practicing using the various teaching/learning tools provided through this ALEKS course. In order to sign up to use ALEKS, you must have an ALEKS access code which can be purchased in the bookstore or you can purchase a subscription through the website. An optional textbook, College Algebra 5th Ed, by Dugopolski is available for purchase in the SCC bookstore. Additionally, you need to have basic computer skills to successfully work on the course materials. System Requirements Please verify that your computer meets the minimum system requirements for this course. This product supports the following operating system and browser combinations:
Algebra I - 01 edition Summary: Covers all the traditional topics teachers want in an algebra curriculum - Introduces all of the field properties along with the properties of equality early and encourages students to use these properties as justifications for solving equations. Provides complete coverage of polynomial operations and all factoring techniques to prepare students for work with rational expressions and quadratic equations later in the course. Thoroughly covers all traditional Algebra 1...show more topics, including work with rational and radical expressions. Optional coverage of proof is also included. ...show less Hardcover Good 0130519669 Good condition, cover has some wear, might have some writings. $2.111720 +$3.99 s/h Acceptable GreenEarthBooks Portland, OR Help save a tree. Buy all your used books from Green Earth Books. Read. Recycle and Reuse! $3.99 +$3.99 s/h Acceptable Borgasorus Books, Inc. MO Wentzville, MO Hardcover Fair 0130519669 Student Edition. No apparent missing pages. Heavy$25.39 +$3.99 s/h Good One Stop Text Books Store Sherman Oaks, CA 2000-07-15 Hardcover87 +$3.99 s/h Acceptable AlphaBookWorks Alpharetta, GA 013051966929.94
Impact Mathematics: Course 3 - 09 edition Summary: IMPACT Mathematicsis designed for grades 6-8 with the goal of completing Algebra 1 content by the end of the 8th grade covering Pre-Algebra and Algebra 1 over 3 years. This program has been extensively field tested and has proven to be highly successful in a large urban district with an increase in assessment scores for all students in all three grade levels. IMPACT Mathematicsmakes the big ideas of mathematics accessible to middle school students through an empha...show moresis on investigation, problem solving, mathematical understanding, and algebra skills. This edition boasts an improved visual design, updated content, and additional NSF-funded performance assessments. The goal ofIMPACT Mathematicsremains to help students develop a deep understanding of mathematics with an emphasis on algebra7.867.87

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