| Preface to the Instructor |
| Note to the Student |
| 1 Functions and Graphs |
| 1.1 Functions |
| 1.2 Types of Functions |
| 1.3 Graphing |
| 1.4 Distance Formula and Slope |
| STATUS CHECK |
| 1.5 More Exercises for Chapter 1 |
| 2 Straight Lines and Conic Sections |
| 2.1 Why Analytic Geometry |
| 2.2 The Straight Line |
| 2.3 The Parabola |
| 2.4 The Ellipse and Circle |
| 2.5 The Hyperbola |
| 2.6 The Second-Degree Equation |
| STATUS CHECK |
| 2.7 More Exercises for Chapter 2 |
| 3 New Coordinate Systems |
| 3.1 Graphing in Three Dimensions |
| 3.2 Polar Coordinates |
| 3.3 Polar Graphs |
| STATUS CHECK |
| 3.4 More Exercises for Chapter 3 |
| 4 The Derivative |
| 4.1 Introduction |
| 4.2 Limits |
| 4.3 The Definition of the Derivative |
| 4.4 General Interpretation of the Derivative |
| 4.5 Differentiating Polynomials |
| 4.6 Differentiating Products and Quotients |
| 4.7 Differentiating Powers of Functions |
| 4.8 Higher-Order Derivatives |
| 4.9 Implicit Differentiation |
| 4.10 Partial Derivatives |
| STATUS CHECK |
| 4.11 More Exercises for Chapter 4 |
| 5 Using the Derivative |
| 5.1 Tangents and Normals |
| 5.2 Curve Sketching |
| 5.3 Maxima and Minima |
| 5.4 Motion |
| 5.5 Related Rates |
| 5.6 Differentials |
| 5.7 Applications of Partial Derivatives |
| STATUS CHECK |
| 5.8 More Exercises for Chapter 5 |
| 6 Integration |
| 6.1 The Indefinite Integral |
| 6.2 Area Under a Curve; the Definite Integral |
| 6.3 The Fundamental Theorem |
| STATUS CHECK |
| 6.4 More Exercises for Chapter 6 |
| 7 Using the Integral |
| 7.1 Indefinite Integral |
| 7.2 Area |
| 7.3 Volume |
| 7.4 Moments |
| 7.5 Fluid Pressure and Force |
| 7.6 Other Applications |
| 7.7 Double Integrals |
| STATUS CHECK |
| 7.8 More Exercises for Chapter 7 |
| 8 Derivatives of Transcendental Functions |
| 8.1 Quick Trigonometry Review |
| 8.2 Derivative of the Sine Function |
| 8.3 Derivatives of Other Trigonometric Functions |
| 8.4 Inverse Trigonometric Functions and Their Derivatives |
| 8.5 Applications |
| 8.6 The Exponential and Logarithmic Functions |
| 8.7 Derivatives of Logarithmic and Exponential Functions |
| 8.8 Applications |
| STATUS CHECK |
| 8.9 More Exercises for Chap |
| 9 Patterns for Integration |
| 9.1 The Power Rule |
| 9.2 The Logarithmic Form |
| 9.3 The Exponential Form |
| 9.4 Basic Trigonometric Forms |
| 9.5 Tricks for Trigonometric Integrals |
| 9.6 Inverse Trigonometric Forms |
| 9.7 Integration by Parts |
| 9.8 Integration by Trigonometric Substitution |
| 9.9 Integration by Partial Functions |
| 9.10 Integration Tables |
| 9.11 Approximate Methods |
| STATUS CHECK |
| 9.12 More Exercises for Chapter 9 |
| 10 Series Expansion of Functions |
| 10.1 Infinite Series |
| 10.2 Maclaurin Series |
| 10.3 Operating with Series |
| 10.4 Computing with Series |
| 10.5 Taylor Series |
| 10.6 Fourier Series |
| STATUS CHECK |
| 10.7 More Exercises for Chapter 10 |
| 11 Differential Equations |
| 11.1 Differential Equations and Their Solutions |
| 11.2 Separation of Variables |
| 11.3 Regrouping to Advantage |
| 11.4 First-Order Linear Differential Equations |
| 11.5 Applications |
| 11.6 Approximation Techniques |
| 11.7 Second-Order Linear Homogeneous Equations |
| 11.8 Repeated or Complex Roots |
| 11.9 Nonhomogeneous Equations |
| 11.10 Applications |
| 11.11 Laplace Transforms |
| 11.12 Differential Equations and Laplace Transforms |
| STATUS CHECK |
| 11.13 More Exercises for Chapter 11 |
| Glossary |
| Appendices |
| 1. Table of Geometric Formulas |
| 2. International System of Units |
| 3. Table of Integrals |
| Answers to Practice Problems |
| Answers to Odd-Numbered Exercises |
| Index |
