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