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Preliminaries | |
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Precalculus Review | |
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Precalculus Review II | |
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the Cartesian Coordinate System | |
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Straight Lines | |
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Functions, Limits, and the Derivative | |
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Functions and Their Graphs | |
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the Algebra of Functions | |
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Functions and Mathematical Models | |
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Limits | |
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One-Sided Limits and Continuity | |
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the Derivative | |
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Differentiation | |
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Basic Rules of Differentiation | |
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the Product and Quotient Rules | |
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the Chain Rule | |
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Marginal Functions in Economics | |
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Higher-Order Derivatives | |
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Implicit Differentiation and Related Rates | |
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Differentials | |
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Applications of the Derivative | |
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Applications of the First Derivative | |
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Applications of the Second Derivative | |
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Curve Sketching | |
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Optimization I | |
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Optimization II | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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Logarithmic Functions | |
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Compound Interest Differentiation of Exponential Functions | |
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Differentiation of Logarithmic Functions | |
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Exponential Functions as Mathematical Models | |
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Integration | |
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Antiderivatives and the Rules of Integration | |
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Integration by Substitution | |
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Area and the Definite Integral | |
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the Fundamental Theorem of Calculus | |
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Evaluating Definite Integrals | |
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Area between Two Curves | |
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Applications of the Definite Integral to Business and Economics | |
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Additional Topics in Integration | |
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Integration by Parts | |
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Integration Using Tables of Integrals | |
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Numerical Integration | |
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Improper Integrals | |
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Volumes of Solids of Revolution | |
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Calculus of Several Variables | |
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Functions of Several Variables | |
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Partial Derivatives | |
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Maxima and Minima of Functions of Several Variables | |
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the Method of Least Squares | |
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Constrained Maxima and Minima and the Method of Lagrange Multipliers | |
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Total Differentials | |
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Double Integrals | |
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Applications of Double Integrals | |
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Differential Equations | |
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Differential Equations | |
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Separation of Variables | |
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Applications of Separable Differential Equations | |
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Approximate Solutions of Differential Equations | |
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Probability and Calculus | |
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Probability Distributions of Random Variables | |
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Expected Value and Standard Deviation | |
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Normal Distributions | |
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Taylor Polynomials and Infinite Series | |
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Taylor Polynomials | |
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Infinite Sequences | |
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Infinite Series | |
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Series with Positive Numbers | |
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Power Series and Taylor Series | |
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More on Taylor Series | |
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Newton's Method | |
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Trigonometric Functions | |
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Measurement of Angles | |
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the Trigonometric Functions | |
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Differentiation of Trigonometric Functions | |
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Integration of Trigonometric Functions | |
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Inverse Functions | |
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The Inverse of a Function | |
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The Graphs of Inverse Functions | |
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Functions that Have Inverses | |
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Finding the Inverse of a Function | |
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Indeterminate Forms and l'H?pital's Rule | |
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Table the Standard Normal Distribution | |
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Answers to Odd-Numbered Exercises | |
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Index | |