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

Published by Pearson (June 15, 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 Late Transcendentals calculus courses (i.e., books with the title “Calculus”).

Calculus Topic: Review of Basics

1. Numbers and Their Disguises

Multiplying and dividing fractions, adding and subtracting fractions, parentheses, 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: Algebraic Functions and Graphs

4. Functions and Their Graphs

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

 

Calculus Topic: Transcendental Functions

5. Cyclic Phenomena: The Six Basic Trigonometric Functions

Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas, graphs of complex trigonometric functions

 

6. Exponential Functions

The family of exponentials, the function ex

 

7. Composition and Inverse Functions

Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression

 

8. Logarithmic Functions

Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm

 

9. Inverse Trigonometric Functions

The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities

 

Calculus Topic: Limits

10. Changing the Form of a Function

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

 

Calculus Topic: Derivatives

11. Simplifying Algebraic Expressions

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

 

Calculus Topic: The Chain Rule

12. Decomposition of Functions

Inner, outer, and outermost functions, decomposing composite functions

 

Calculus Topic: Implicit Differentiation

13. Equations of Degree 1 Revisited

Solving linear equations involving derivatives

 

Calculus Topic: Related Rates, Applied Max-Min Problems

14. Word Problems, Algebraic and Transcendental

Applied Max-Min 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, exponential growth and decay

 

Calculus Topic: Integrating Trigonometric Functions

15. Trigonometric Identities

Rewriting trigonometric expressions using identities.

 

Appendices

A. The Binomial Theorem

B. Derivation of The Quadratic Formula

 

Answers to Exercises

Index

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