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| Note: Chapters 110 conclude with an Algebra Review, a Chapter Summary and Study Strategies, Review Exercises, and Sample Post-Graduation Exam Questions. A Word from the Authors (Preface) Features A Plan for You as a Student (Study Strategies) | |
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| A Precalculus Review | |
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| The Real Line and Order | |
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| Absolute Value and Distance on the Real Line | |
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| Exponents and Radicals | |
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| Factoring Polynomials | |
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| Fractions and Rationalization | |
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| Functions, Graphs, and Limits | |
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| The Cartesian Plane and the Distance Formula | |
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| Graphs of Equations | |
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| Lines in the Plane and Slope | |
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| Functions | |
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| Limits | |
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| Continuity | |
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| Differentiation | |
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| The Derivative and the Slope of a Graph | |
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| Some Rules for Differentiation | |
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| Rates of Change: Velocity and Marginals | |
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| The Product and Quotient Rules | |
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| The Chain Rule | |
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| Higher-Order Derivatives | |
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| Implicit Differentiation | |
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| Related Rates | |
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| Applications of the Derivative | |
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| Increasing and Decreasing Functions | |
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| Extrema and the First-Derivative Test | |
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| Concavity and the Second-Derivative Test | |
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| Optimization Problems | |
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| Business and Economics Applications | |
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| Asymptotes | |
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| Curve Sketching: A Summary | |
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| Differentials and Marginal Analysis | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions | |
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| Natural Exponential Functions | |
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| Derivatives of Exponential Functions | |
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| Logarithmic Functions | |
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| Derivatives of Logarithmic Functions | |
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| Exponential Growth and Decay | |
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| Integration and Its Applications | |
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| Antiderivatives and Indefinite Integrals | |
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| The General Power Rule | |
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| Exponential and Logarithmic Integrals | |
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| Area and the Fundamental Theorem of Calculus | |
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| The Area of a Region Bounded by Two Graphs | |
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| The Definite Integral as the Limit of a Sum | |
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| Volumes of Solids of Revolution | |
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| Techniques of Integration | |
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| Integration by Substitution | |
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| Integration by Parts and Present Value | |
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| Partial Fractions and Logistic Growth | |
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| Integration Tables and Completing the Square | |
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| Numerical Integration | |
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| Improper Integrals | |
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| Functions of Several Variables | |
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| The Three-Dimensional Coordinate System | |
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| Surfaces in Space | |
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| Functions of Several Variables | |
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| Partial Derivatives | |
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| Extrema of Functions of Two Variables | |
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| Lagrange Multipliers | |
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| Least Squares Regression Analysis | |
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| Double Integrals and Area in the Plane | |
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| Applications of Double Integrals | |
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| Trigonometric Functions | |
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| Radian Measure of Angles | |
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| The Trigonometric Functions | |
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| Graphs of Trigonometric Functions | |
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| Derivatives of Trigonometric Functions | |
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| Integrals of Trigonometric Functions | |
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| L'Hocirc;pital's Rule | |
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| Probability and Calculus | |
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| Discrete Probability | |
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| Continuous Random Variables | |
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| Expected Value and Variance | |
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| Series and Taylor Polynomials | |
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| Sequences | |
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| Series and Convergence | |
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| p-Series and the Ratio Test | |
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| Power Series and Taylor's Theorem | |
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| Taylor Polynomials | |
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| Newton's Method | |
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| Appendices | |
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| Alternate Introduction to the Fundamental Theorem of Calculus | |
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| Formulas | |
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| Differential Equations | |
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| Solutions of Differential Equations | |
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| Separation of Variables | |
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| First-Order Linear Differential Equations | |
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| Applications of Differential Equations | |
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| Properties and Measurement | |
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| Graphing Utility Programs | |