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| Introduction to Analytic Geometry | |
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| The Cartesian Coordinate System | |
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| The Slope | |
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| The Straight Line | |
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| Curve Sketching | |
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| Discussion of Curves with Graphing Utilities | |
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| The Conics | |
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| The Circle | |
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| The Parabola | |
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| The Ellipse | |
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| The Hyperbola | |
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| Translation of Axes | |
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| Standard Equations of the Conics | |
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| Review Exercises | |
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| Introduction to Calculus: The Derivative | |
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| Functions and Intervals | |
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| Limits | |
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| The Derivative | |
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| The Derivative by the Four-Step Process | |
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| Derivatives of Polynomials | |
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| Instantaneous Rates of Change | |
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| Differentiation Formulas | |
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| Implicit Differentiation | |
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| Higher Derivatives | |
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| Review Exercises | |
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| Applications of the Derivative | |
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| The First-Derivative Test | |
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| The Second-Derivative Test | |
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| Exploring with Graphing Utilities | |
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| Applications of Minima and Maxima | |
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| Related rates | |
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| Differentials | |
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| Review Exercises | |
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| The Integral | |
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| Antiderivatives | |
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| The Area Problem | |
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| The Fundamental Theorem of Calculus | |
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| The Integral: Notation and General Definition | |
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| Basic Integration Formulas | |
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| Area Between Curves | |
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| Improper Integrals | |
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| The Constant of Integration | |
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| Numerical Integration | |
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| Review Exercises | |
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| Application of the Integral | |
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| Means of Root Mean Squares | |
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| Volumes of Revolution: Disk and Washer Methods | |
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| Volumes of Revolution: Shell Method | |
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| Centroids | |
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| Moments of Inertia | |
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| Work and Fluid Pressure | |
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| Review Exercises | |
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| Derivatives of Transcendental Functions | |
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| Review of Trigonometry | |
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| Derivatives of Sine and Cosine Functions | |
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| Other Trigonometric Functions | |
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| Inverse Trigonometric Functions | |
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| Derivatives of Inverse Trigonometric Functions | |
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| Exponential and Logarithmic Functions | |
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| Derivative of the Logarithmic Function | |
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| Derivative of the Exponential Function | |
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| L'Hospital's rule | |
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| Applications | |
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| Newton's Method | |
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| Review Exercises | |
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| Integration Techniques | |
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| The Power Formula Again | |
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| The Logarithmic and Exponentials Forms | |
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| Trigonometric Forms | |
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| Further Trigonometric Forms | |
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| Inverse Trigonometric Forms | |
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| Integration by Trigonometric Substitution | |
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| Integration by Parts | |
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| Integration of Rational Functions | |
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| Integration by Use of Tables | |
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| Additional Remarks | |
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| Review Exercises | |
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| Parametic Equations, Vectors, and Polar Coordinates | |
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| Vectors and Parametric Equations | |
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| Arc Length | |
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| Polar Coordinates | |
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| Curves in Polar Coordinates | |
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| Areas in Polar Coordinates | |
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| Review Exercises | |
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| Three-Dimensional Space; Partial Derivatives; Multiple Integrals | |
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| Surfaces in Three Dimensions | |
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| Partial Derivatives | |
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| Applications of Partial Derivatives | |
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| Curve Fitting | |
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| Integrated Integrals | |
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| Volumes by Double Integration | |
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| Mass, Centroids, and Moments of Inertia | |
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| Volumes in Cylindrical Coordinates | |
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| Review Exercises | |
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| Infinite Series | |
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| Introduction to Infinite Series | |
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| Tests for Convergence | |
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| Maclaurin Series | |
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| Operations with Series | |
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| Computations with Series | |
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| Applications | |
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| Fourier Series | |
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| Review Exercises | |
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| First-Order Differetial Equations | |
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| What is Differential Equation? Separation of Variables | |
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| First-Order Linear Differential Equations | |
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| Applications of First-Order Differential Equations | |
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| Numerical Solutions | |
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| Review Exercises | |
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| Higher Order Linear Differential Equations | |
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| Higher-Order Homogeneous Differential Equations | |
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| Auxiliary Equations with Repeating or Complex Roots | |
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| Nonhomogeneous Equations | |
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| Applications of Second-Order Equations | |
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| Review Exercises | |
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| The Laplace Transform | |
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| Introduction and Basic Properties | |
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| Inverse Laplace Transforms | |
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| Partial Fractions | |
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| Solutions of Linear Equations by Laplace Transforms | |
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| Review Exercises | |
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| Tables | |
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| Common Units of Measure | |
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| A Short Table of Integrals | |
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| Answers to Selected Exercises | |
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| Index | |