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1. Functions 1.1 Review of Functions 1.2 Representing Functions 1.3 Inverse, Exponential, and Logarithmic Functions 1.4 Trigonometric Functions and Their Inverses Review Exercises 2. Limits 2.1 The Idea of Limits 2.2 Definitions of Limits 2.3 Techniques for Computing Limits 2.4 Infinite Limits 2.5 Limits at Infinity 2.6 Continuity 2.7 Precise Definitions of Limits Review Exercises 3. Derivatives 3.1 Introducing the Derivative 3.2 The Derivative as a Function 3.3 Rules of Differentiation 3.4 The Product and Quotient Rules 3.5 Derivatives of Trigonometric Functions 3.6 Derivatives as Rates of Change 3.7 The Chain Rule 3.8 Implicit Differentiation 3.9 Derivatives of Logarithmic and Exponential Functions 3.10 Derivatives of Inverse Trigonometric Functions 3.11 Related Rates Review Exercises 4. Applications of the Derivative 4.1 Maxima and Minima 4.2 Mean Value Theorem 4.3 What Derivatives Tell Us 4.4 Graphing Functions 4.5 Optimization Problems 4.6 Linear Approximation and Differentials 4.7 L’Hôpital’s Rule 4.8 Newton’s Method 4.9 Antiderivatives Review Exercises 5. Integration 5.1 Approximating Areas under Curves 5.2 Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with Integrals 5.5 Substitution Rule Review Exercises 6. Applications of Integration 6.1 Velocity and Net Change 6.2 Regions Between Curves 6.3 Volume by Slicing 6.4 Volume by Shells 6.5 Length of Curves 6.6 Surface Area 6.7 Physical Applications Review Exercises 7. Logarithmic, Exponential, and Hyperbolic Functions 7.1 Logarithmic and Exponential Functions Revisited 7.2 Exponential Models 7.3 Hyperbolic Functions Review Exercises 8. Integration Techniques 8.1 Basic Approaches 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitutions 8.5 Partial Fractions 8.6 Integration Strategies 8.7 Other Methods of Integration 8.8 Numerical Integration 8.9 Improper Integrals Review Exercises 9. Differential Equations 9.1 Basic Ideas 9.2 Direction Fields and Euler’s Method 9.3 Separable Differential Equations 9.4 Special First-Order Linear Differential Equations 9.5 Modeling with Differential Equations Review Exercises 10. Sequences and Infinite Series 10.1 An Overview 10.2 Sequences 10.3 Infinite Series 10.4 The Divergence and Integral Tests 10.5 Comparison Tests 10.6 Alternating Series 10.7 The Ratio and Root Tests 10.8 Choosing a Convergence Test Review Exercises 11. Power Series 11.1 Approximating Functions with Polynomials 11.2 Properties of Power Series 11.3 Taylor Series 11.4 Working with Taylor Series Review Exercises 12. Parametric and Polar Curves 12.1 Parametric Equations 12.2 Polar Coordinates 12.3 Calculus in Polar Coordinates 12.4 Conic Sections Review Exercises Appendix A. Proofs of Selected Theorems Appendix B. Algebra Review ONLINE Appendix C. Complex Numbers ONLINE Answers Index Table of Integrals Table of Contents
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