Just-in-Time Algebra and Trigonometry for Calculus
Produktdetaljer
Biografisk notat
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!”
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!
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- 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.
Produktdetaljer
Biografisk notat
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!”