Just-in-Time Algebra and Trigonometry for Calculus

<p style="MARGIN: 0px">Calculus Topic: Review of Basics</p> <p style="MARGIN: 0px">1. Numbers and Their Disguises</p> <p style="MARGIN: 0px">Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Circles, Parabolas, etc.</p> <p style="MARGIN: 0px">2. Completing the Square</p> <p style="MARGIN: 0px">Completing the square in one and two variables</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Equations</p> <p style="MARGIN: 0px">3. Solving Equations</p> <p style="MARGIN: 0px">Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Functions and Graphs</p> <p style="MARGIN: 0px">4. Functions and Their Graphs</p> <p style="MARGIN: 0px">Introduction, equations of lines, power functions, shifting graphs, intersection of curves</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Limits</p> <p style="MARGIN: 0px">5. Changing the Form of a Function</p> <p style="MARGIN: 0px">Factoring, canceling, long division, rationalizing, extracting a factor from under a radical</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Derivatives</p> <p style="MARGIN: 0px">6. Simplifying Algebraic Expressions</p> <p style="MARGIN: 0px">Working with difference quotients and rational functions, canceling common factors, rationalizing expressions</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Derivatives of Trigonometric Functions</p> <p style="MARGIN: 0px">7. Cyclic Phenomena: The Six Basic Trigonometric Functions</p> <p style="MARGIN: 0px">Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x, graphs of complex trigonometric functions</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: The Chain Rule</p> <p style="MARGIN: 0px">8. Composition and Decomposition of Functions</p> <p style="MARGIN: 0px">Composite functions, inner, outer, and outermost functions, decomposing composite functions</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Implicit Differentiation</p> <p style="MARGIN: 0px">9. Equations of Degree 1 Revisited</p> <p style="MARGIN: 0px">Solving linear equations involving derivatives</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Related Rates, Applied Max-Min Problems</p> <p style="MARGIN: 0px">10. Word Problems</p> <p style="MARGIN: 0px">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</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Calculus Topic: Integrating Trigonometric Functions</p> <p style="MARGIN: 0px">11. Trigonometric Identities</p> <p style="MARGIN: 0px">Rewriting trigonometric expressions using identities</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Appendices</p> <p style="MARGIN: 0px">A. Exponential Functions</p> <p style="MARGIN: 0px">B. Inverse Functions</p> <p style="MARGIN: 0px">C. Logarithmic Functions</p> <p style="MARGIN: 0px">D. Inverse Trigonometric Functions</p> <p style="MARGIN: 0px">E. The Binomial Theorem</p> <p style="MARGIN: 0px">E. Derivation of the Quadratic Formula</p> <p style="MARGIN: 0px">&nbsp;</p> <p style="MARGIN: 0px">Answers to Exercises</p>Index