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

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

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