# Just-in-Time Algebra and Trigonometry for Early Transcendentals Calculus

**by**Mueller, Guntram; Brent, Ronald I.

### 9780321671035

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## Summary

## Author Biography

**Guntram B. Mueller **received his PhD in Mathematics from the University of Notre Dame. He has taught calculus many times and is very familiar with the typical strengths and weaknesses in the backgrounds of his students. That experience is what guided him, in cooperation with Dr. Ron Brent, in writing the Just-in-Time series. His advice? Buy the book! It's got just what you need, just in time.

**Ronald I. Brent**is a Professor of Mathematics at University of Massachusetts, Lowell, where he has taught since 1987. He earned his PhD in Mathematics from Rensselaer Polytechnic Institute. Dr. Brent is the author of many publications, including three Just-In-Time mathematics texts. His main advice to his calculus students is: “Work on your homework as if your life in this course depends upon it.

*Because it does!*”

## Table of Contents

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 *e ^{x} *

**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