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Functions Modeling Change: A Preparation for Calculus, 2nd Texas Edition

ISBN: 978-0-470-03919-9
608 pages
April 2006, ©2007
Functions Modeling Change: A Preparation for Calculus, 2nd Texas Edition (0470039191) cover image
Developed by the Consortium based at Harvard University and funded by a National Science Foundation Grant, this revised edition is designed for use in conjunction with the High School Precalculus requirements of the Texas State Standards. The text is developed to provide students with the foundation they need to succeed in Calculus as an advanced High School student or an entering University student. It’s approach is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. It provides verbal, algebraic, visual and numerical points of view to give students another way of mastering the material. A large number of real-world examples and problems enable students to create mathematical models that will help them understand the world in which they live.
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1. Functions, Lines, and Change.

2. Functions, Quadratics, and Concavity.

3. Exponential Functions.

4. Logarithmic Functions.

5. Transformations of Functions and Their Graphs.

6. Trigonometric Functions.

7. Trigonometry.

8. Compositions, Inverses, and Combinations of Functions.

9. Polynomial and Rational Functions.

10. Vectors and Matrices.

11. Sequences and Series.

12. Parametric Equations and Conic Sections.

Answers to Odd-Numbered Problems.

Index.

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  • The first 3 chapters from the first edition have been consolidated into 2 chapters. Streamlined review topics allow professors to get to function notation much sooner after the concept of a function has been introduced
  • Algebra review has been integrated throughout the text, mostly in exercises but also in explanations. More skill building has been emphasized wherever appropriate. The algebraic tools used in a chapter have been summarized for easy reference in a "Tools" section at the end of the chapter.
  • Exercises sets are now divided into basic (Exercises) and conceptual (Problems) categories. Data and exercises have been updated and revised as appropriate.
  • There is a new exercise category: True/False "Check Your Understanding."
  • Inverses are emphasized more in the new chapter 2 (former chapter 3) for a better link to their use in later chapters.
  • Right triangle trigonometry is introduced earlier, in the Tools section at the end of chapter 6.
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  • The Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally.
  • Functions as models of change is the central theme.
  • Exceptional Problems: Examples and problems based on real data help students create mathematical models to help them understand their world. An appropriate number of drill problems are included to assist students in learning techniques. The problems are varied and some are more challenging. Most cannot be done by following a template in the text.
  • Allows for a broad range of teaching styles. This text is flexible enough for use in large lecture halls, small classes, or in group or lab settings.
  • Focuses on fewer topics than is customary, but each topic is treated in greater depth. Only those topics essential to the study of calculus are included.
  • Reflects the spirit of the standards established by the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC), and meets the recommendations of the National Council of Teachers of Mathematics (NCTM)
  • Assumes technology has a place in modern mathematics. This text takes full advantage of technology when appropriate, although no specific technology is emphasized. It is important for students to learn how and when to use technology as a tool, as well as its limitations. However the focus of the text is on conceptual understanding not technology.
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