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Just-in-Time Algebra and Trigonometry for Calculus, 4th edition

Published by Pearson (July 17, 2012) © 2013

  • Guntram Mueller
  • Ronald Brent
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This book is designed for current calculus students to review the algebra and trigonometry skills that are so crucial for success in calculus. Organized to correspond to a typical calculus course, relevant algebra and trigonometry topics are presented just as students need them, with warnings about pitfalls and exercise sets for practice. Whether used as a reference or for catching up, this text will prove invaluable for all students taking calculus.

Note: a different version of this book is available specifically for Early Transcendentals calculus courses.

Calculus Topic: Review of Basics

1. Numbers and Their Disguises

Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals

 

Calculus Topic: Circles, Parabolas, etc.

2. Completing the Square

Completing the square in one and two variables

 

Calculus Topic: Equations

3. Solving Equations

Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property

 

Calculus Topic: Functions and Graphs

4. Functions and Their Graphs

Introduction, equations of lines, power functions, shifting graphs, intersection of curves

 

Calculus Topic: Limits

5. Changing the Form of a Function

Factoring, canceling, long division, rationalizing, extracting a factor from under a radical

 

Calculus Topic: Derivatives

6. Simplifying Algebraic Expressions

Working with difference quotients and rational functions, canceling common factors, rationalizing expressions

 

Calculus Topic: Derivatives of Trigonometric Functions

7. Cyclic Phenomena: The Six Basic Trigonometric Functions

Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x, graphs of complex trigonometric functions

 

Calculus Topic: The Chain Rule

8. Composition and Decomposition of Functions

Composite functions, inner, outer, and outermost functions, decomposing composite functions

 

Calculus Topic: Implicit Differentiation

9. Equations of Degree 1 Revisited

Solving linear equations involving derivatives

 

Calculus Topic: Related Rates, Applied Max-Min Problems

10. Word Problems

Algebraic word problems; the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines

 

Calculus Topic: Integrating Trigonometric Functions

11. Trigonometric Identities

Rewriting trigonometric expressions using identities

 

Appendices

A. Exponential Functions

B. Inverse Functions

C. Logarithmic Functions

D. Inverse Trigonometric Functions

E. The Binomial Theorem

E. Derivation of the Quadratic Formula

 

Answers to Exercises

Index

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