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
