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
