Just-in-Time Algebra and Trigonometry for Calculus

Description

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.

 

• Chapter 5 now includes a new section on Graphs of Trigonometric Functions, along with exercises to go with this topic.
• Additional exercises in chapters 10 and 11 give students more of the practice they need to master the concepts.
• A Getting Ready for Calculus chapter is available online for students using a MyMathLab with a Pearson calculus text.
• Hundreds of additional practice problems correspond to topics covered in Just-In-Time Algebra and Trigonometry for Calculus.
• Use this online chapter to diagnose gaps in prerequisite skills and provide students with a review at the beginning of the course or remediation throughout the semester.
• MyMathLab is available to qualified adopters. Learn more at www.mymathlab.com or contact your Pearson representative.

 

Are you ready to ace calculus at the college level? With this book, you will be! Professors often say “Students don’t fail the calculus, they fail the algebra.” In other words, even if you understand calculus, your algebra and trigonometry skills can hold you back. Here’s a quick quiz—do you remember how to:

• Factor trinomials?
• Solve equations containing exponents and logs?
• Work with inverse trig functions?

 

If not, that’s where this book comes in handy! Just-in-Time is designed to bolster the algebra and trigonometry skills you’ll need while you study calculus. As you make your way through the course, Just-in-Time is with you every step of the way, showing you the exact algebra or trigonometry topics that you’ll need and pointing out potential problem spots. The easy-to-use Table of Contents features the calculus subject listed directly across from the algebra/trigonometry skills needed to master that topic. Use this book as your study companion and put your anxiety to rest!

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!”

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

• Topics are ordered to correspond to a typical calculus course, for instance, the topic “composition and decomposition of functions” is listed as a prerequisite for the Chain Rule.

• Extensive exercise sets, especially in the sections on word problems, exponentials, and logarithms, give more opportunities for both students and instructors to tailor exercises to their specific needs.
• Precisely written text makes the concepts clear and gives students what they need to succeed in calculus.
• Odd-numbered exercises have answers in the back of the book. Answers to the even-numbered exercises are available to professors on Pearson’s Instructor Resource Center.