Functions Modeling Change: A Preparation for Calculus / Edition 4

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From the Calculus Consortium based at Harvard University, this comprehensible book prepares readers for the study of calculus, presenting families of functions as models for change. These materials stress conceptual understanding and multiple ways of representing mathematical ideas.
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Editorial Reviews

From the Publisher
“Additionally, a large number of real-world applications, examples, and problems enable students to create mathematical models that relate to the world around them.” (Zentralblatt MATH, 1 March 2015)
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Product Details

  • ISBN-13: 9780470484746
  • Publisher: Wiley
  • Publication date: 11/23/2010
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 672
  • Sales rank: 671,161
  • Product dimensions: 8.20 (w) x 10.60 (h) x 0.90 (d)

Meet the Author

Eric Connally is a Professor of Mathematics at Harvard University Extension in Cambridge, Massachusetts.

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Table of Contents

Table of Contents.
1 Functions and Change.
1.1 What is a Function?
1.2 Proportions and Rates.
1.3 Rate of Change.
Review Problems.
2 Linear Functions.
2.1 What Makes a Function Linear?
2.2 Formulas for Linear Functions.
2.3 Geometric Properties of Linear Functions.
2.4 Fitting Linear Functions to Data.
Review Problems.
3 Function Notation.
3.1 Input and Output.
3.2 Changes in Input and Output.
3.3 Domain and Range.
3.4 Piecewise Defined Functions.
Review Problems.
4 Exponential and Logarithmic Functions.
4.1 Introduction to the Family of Exponential Functions.
4.2 Comparing Exponential and Linear Functions.
4.3 Exponential Graphs and Concavity.
4.4 Logarithms and their Properties.
4.5 The Logarithmic Function.
4.6 Logarithms and Exponential Models.
4.7 Continuous Growth and the Number e.
4.8 Compound Interest.
4.9 Logarithmic Scales.
4.10 Fitting Curves to Data.
Review Problems.
5 Transformations of Functions and their Graphs.
5.1 Vertical and Horizontal Shifts.
5.2 Reflections and Symmetry.
5.3 Vertical Stretches and Compressions.
5.4 Horizontal Stretches and Compressions.
5.5 The Family of Quadratic Functions.
Review Problems.
6 Trigonometric Functions.
6.1 Introduction to Periodic Functions.
6.2 The Sine and Cosine Functions.
6.3 Radians.
6.4 Graphs of the Sine and Cosine.
6.5 Sinusoidal Functions.
6.6 Other Trigonometric Functions.
6.7 Inverse Trigonometric Functions.
Review Problems.
7 Trigonometry.
7.1 Right Triangles.
7.2 Non-Right Triangles: Laws of Sines and Cosines.
7.3 Trigonometric Identities.
7.4 Sum and Difference Formulasfor Sine and Cosine.
7.5 Trigonometric Models.
7.6 Polar Coordinates.
Review Problems.
8 Compositions, Inverses, and Combinations of Functions.
8.1 Composition of Functions.
8.2 Inverse Functions.
8.3 Combinations of Functions.
Review Problems.
9 Polynomial and Rational Functions.
9.1 Power Functions.
9.2 Comparing Power, Exponential, and Log Functions.
9.3 Polynomial Functions.
9.4 The Short-Run Behavior of Polynomials.
9.5 Rational Functions.
9.6 The Short-Run Behavior of Rational Functions.
Review Problems.
10 Vectors.
10.1 Vectors.
10.2 The Components of a Vector.
10.3 Application of Vectors.
10.4 The Dot Product.
Review Problems.
11 Other Ways of Defining Functions.
11.1 Defining Functions Using Sums.
11.2 Geometric Series.
11.3 Parametric Equations.
11.4 Implicitly Defined Curves and Conic Sections.
11.5 Complex Numbers and Polar Coordinates.
11.6 Hyperbolic Functions.
Review Problems.
A Exponents.
B Multiplying Algebraic Expressions.
C Factoring Algebraic Expressions.
D Working with Fractions.
E Changing the Form of Expressions.
F Solving Equations.
G Systems of Equations.
H Inequalities.
Answers to Odd Numbered Problems.
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  • Anonymous

    Posted May 23, 2002

    Very Sinsable Math Book

    A math book that had good examples and was readily followable by my 11th grader. Problems made sense but was a little weak on trig idenities. Why do they have to make the books so large now? When I was in school, the books were half the size and contained the same or more info. The large size not only increases the price, but gives students a bad back from carring these made large to impress books.

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted December 16, 1999

    Frustration should be the title of this book

    I am a student who has many problems with this book. The ideas are very confusing to a student. I have had students at level two calculus try to help me with some problems and they too find it frustrating!

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