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Just-In-Time Algebra and Trigonometry for Students of Calculus,9780321269430

Just-In-Time Algebra and Trigonometry for Students of Calculus

by ;
Edition:
3rd
ISBN13:

9780321269430

ISBN10:
0321269438
Format:
Paperback
Pub. Date:
9/23/2004
Publisher(s):
Pearson
List Price: $27.60

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Summary

Strong Algebra and Trigonometry skills are crucial to success in calculus. This text is designed to bolster these skills while students study calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra or trigonometry topics and points out potential problem spots. The table of contents is organized so that the algebra and trigonometry topics are arranged in the order in which they are needed for calculus. The exponential, log, and inverse trigonometric functions are given in the appendices, to be used as the need arises in the particular calculus text used in the course. #xA0; Topics include: 1. Numbers and Their Disguises 2. Completing the Square 3. Solving Equations 4. Functions and Their Graphs 5. Changing the Form of a Function 6. Simplifying Algebraic Expressions 7. Cyclic Phenomena: The Six Basic Trigonometric Functions 8. Composition and Decomposition of Functions 9. Equations of Degree 1 Revisited 10. Word Problems 11. Trigonometric Identities #xA0;

Author Biography

Guntram B. Mueller received his Ph.D. in Mathematics (Theory of Functions of Several Complex Variables) in 1971 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 Ph.D. in Mathematics from Renssalaer 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 Subjects (What you'll take)
Algebra and Trigonometry Background (What you'll need)
Review of Basics
Numbers and Their Disguises
Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals
1(24)
Circles, Parabolas, etc.
Completing the Square
Completing the square in one and two variables
25(5)
Equations
Solving Equations
Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property
30(17)
Functions and Graphs
Functions and Their Graphs
Introduction, equations of lines, power functions, shifting graphs, intersection of curves
47(28)
Limits
Changing the Form of a Function
Factoring, canceling, long division, rationalizing, extracting a factor from under a radical
75(14)
Derivatives
Simplifying Algebraic Expressions
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions
89(7)
Derivatives of Trig Functions
Cyclic Phenomena: The Six Basic Trigonometric Functions
Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x
96(20)
The Chain Rule
Composition and Decomposition of Functions
Composite functions; inner, outer, and outermost functions: decomposing composite functions
116(4)
Implicit Differentiation
Equations of Degree 1 Revisited
Solving linear equations involving derivatives
120(4)
Related Rates, Applied Max-Min Problems
Word Problems, Algebraic and Trigonometric
Algebraic word problems; the geometry of rectangles, circles, and spheres; trigonometric word problems; right angled triangles; the law of sines and the law of cosines
124(12)
Integrating Trigonometric Functions
Trigonometric Identities
Rewriting trigonometric expressions using identities
136(5)
Appendices (Use as needed)
A. Exponential Functions
141(6)
B. Inverse Functions
147(9)
C. Logarithmic Functions
156(13)
D. Inverse Trigonometric Functions
169(13)
E. The Binomial Theorem
182(3)
F. Derivation of the Quadratic Formula
185(2)
Answers to Odd-Numbered Exercises 187(21)
Index 208


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