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| Precalculus Review | |
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| Real Numbers | |
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| Exponents and Radicals | |
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| Multiplying and Factoring Algebraic Equations | |
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| Rational Expressions | |
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| Solving Polynomial Equations | |
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| Solving Miscellaneous Equations | |
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| The Coordinate Plane | |
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| Functions and Linear Models | |
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| Functions from the Numerical, Algebraic, and Graphical Viewpoints | |
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| Applications: Functions and Models | |
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| Linear Functions and Models | |
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| Linear Regression | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Modeling Spending on Internet Advertising | |
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| Technology Guides | |
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| Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |
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| Nonlinear Functions and Models | |
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| Quadratic Functions and Models | |
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| Exponential Functions and Models | |
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| Logarithmic Functions and Models | |
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| Logistic Functions and Models | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Checking up on Malthus | |
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| Technology Guides | |
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| Optional Internet Topics: Inverse Functions | |
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| Using and Deriving Algebraic Properties of Logarithms | |
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| Introduction to the Derivative | |
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| Limits: Numerical and Graphical Approaches | |
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| Limits and Continuity | |
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| Limits: Algebraic Approach | |
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| Average Rate of Change | |
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| Derivatives: Numerical and Graphical Viewpoints | |
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| Derivatives: Algebraic Viewpoint | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Reducing Sulfur Emissions | |
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| Technology Guides | |
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| Optional Internet Topics: Sketching the Graph of the Derivative | |
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| Proof of the Power Rule | |
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| Continuity and Differentiability | |
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| Techniques of Differentiation with Applications | |
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| Derivatives of Powers, Sums, and Constant Multiples | |
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| A First Application: Marginalnalysis | |
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| The Product and Quotient Rules | |
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| The Chain Rule | |
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| Derivatives of Logarithmic and Exponential Functions | |
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| Implicit Differentiation | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Projecting Market Growth | |
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| Technology Guides | |
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| Optional Internet Topic: Linear Approximation and Error Estimation | |
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| Further Applications of the Derivative | |
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| Maxima and Minima | |
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| Applications of Maxima and Minima | |
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| Higher Order Derivatives: Acceleration and Concavity | |
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| Analyzing Graphs | |
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| Related Rates | |
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| Elasticity | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Production Lot Size Management | |
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| Technology Guides | |
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| The Integral | |
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| The Indefinite Integral | |
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| Substitution | |
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| The Definite Integral: Numerical and Graphical Approaches | |
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| The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Wage Inflation | |
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| Technology Guides | |
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| Optional Internet Topic: Numerical Integration | |
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| Further Integration Techniques and Applications of the Integral | |
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| Integration by Parts | |
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| Area Between Two Curves and Applications | |
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| Averages and Moving Averages | |
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| Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams | |
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| Improper Integrals and Applications | |
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| Differential Equations and Applications | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Estimating Tax Revenues | |
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| Technology Guides | |
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| Optional Internet Topic: Taylor Polynomials | |
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| Functions of Several Variables | |
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| Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints | |
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| Partial Derivatives | |
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| Maxima and Minima | |
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| Constrained Maxima and Minima and Applications | |
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| Double Integrals and Applications | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Modeling Household Income | |
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| Technology Guides | |
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| Optional Internet Topic: The Chain Rule for Functions of Several Variables | |
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| Trigonometric Models | |
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| Trigonometric Functions, Models, and Regression | |
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| Derivatives of Trigonometric Functions and Applications | |
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| Integrals of Trigonometric Functions and Applications | |
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| Key Concepts | |
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| Review Exercises | |
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| Case Study: Predicting Cocoa Inventories | |
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| Technology Guides | |
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| Answers to Selected Exercises | |
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| Index | |
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| Optional Internet Topic | |
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| S. Calculus Applied to Probability and Statistics | |
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| Introduction | |
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| Continuous Random Variables and Histograms | |
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| Probability Density Functions: Uniform, Exponential, Normal, and Beta | |
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| Mean, Median, Variance and Standard Deviation | |
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| Case Study: Creating a Family Trust | |