Just-in-time algebra and trigonometry for students of calculus (3rd ed )
Auteurs : BRENT Ronald, MUELLER Guntram
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.
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
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 FunctionsB. Inverse FunctionsC. Logarithmic Functions D. Inverse Trigonometric FunctionsE. The Binomial TheoremE. Derivation of the Quadratic Formula
Answers to Exercises
Index
Date de parution : 04-2005
Ouvrage de 224 p.
