Orientation Quizzes.-
R Review of Fundamentals.-
R.1 Basic Algebra: Real Numbers and Inequalities.-
R.2 Intervals and Absolute Values.-
R.3 Laws of Exponents.-
R.4 Straight Lines.-
R.5 Circles and Parabolas.-
R.6 Functions and Graphs.-
1 Derivatives and Limits.-
1.1 Introduction to the Derivative.-
1.2 Limits.-
1.3 The Derivative as a Limit and the Leibniz Notation.-
1.4 Differentiating Polynomials.-
1.5 Products and Quotients.-
1.6 The Linear Approximation and Tangent Lines.-
2 Rates of Change and the Chain Rule.-
2.1 Rates of Change and the Second Derivative.-
2.2 The Chain Rule.-
2.3 Fractional Powers and Implicit Differentiation.-
2.4 Related Rates and Parametric Curves.-
2.5 Antiderivatives.-
3 Graphing and Maximum—Minimum Problems.-
3.1 Continuity and the Intermediate Value Theorem.-
3.2 Increasing and Decreasing Functions.-
3.3 The Second Derivative and Concavity.-
3.4 Drawing Graphs.-
3.5 Maximum—Minimum Problems.-
3.6 The Mean Value Theorem.-
4 The Integral.-
4.1 Summation.-
4.2 Sums and Areas.-
4.3 The Definition of the Integral.-
4.4 The Fundamental Theorem of Calculus.-
4.5 Definite and Indefinite Integrals.-
4.6 Applications of the Integral.-
5 Trigonometric Functions.-
5.1 Polar Coordinates and Trigonometry.-
5.2 Differentiation of the Trigonometric Functions.-
5.3 Inverse Functions.-
5.4 The Inverse Trigonometric Functions.-
5.5 Graphing and Word Problems.-
5.6 Graphing in Polar Coordinates.-
6 Exponentials and Logarithms.-
6.1 Exponential Functions.-
6.2 Logarithms.-
6.3 Differentiation of the Exponential and Logarithmic Functions.-
6.4 Graphing and Word Problems.-
Answers A.1.-
Index I.1.
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