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

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!”

1. Numbers and Their Disguises


Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals



2. Completing the Square


Completing the square in one and two variables



3. Solving Equations


Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property



4. Functions and Their Graphs


Introduction, equations of lines, power functions, shifting graphs, intersection of curves



5. Changing the Form of a Function


Factoring, canceling, long division, rationalizing, extracting a factor from under a radical



6. Simplifying Algebraic Expressions


Working with difference quotients and rational functions, canceling common factors, rationalizing expressions



7. Cyclic Phenomena: The Six Basic Trigonometric Functions


Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x



8. Composition and Decomposition of Functions


Composite functions, inner, outer, and outermost functions, decomposing composite functions



9. Equations of Degree 1 Revisited


Solving linear equations involving derivatives



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



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