Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises | |
Preface A User's Guide to Features Integrating Excel Graphing Calculator Terminology | |
Functions | |
Real Numbers, Inequalities, and Lines | |
Exponents | |
Functions | |
Functions, Continued | |
Derivatives and Their Uses | |
Limits and Continuity | |
Rates of Change, Slopes, and Derivatives | |
Some Differentiation Formulas | |
The Product and Quotient Rules | |
Higher–Order Derivatives | |
The Chain Rule and the Generalized Power Rule | |
Nondifferentiable Functions | |
Further Applications of Derivatives | |
Graphing Using the First Derivative | |
Graphing Using the First and Second Derivatives | |
Optimization | |
Further Applications of Optimization | |
Optimizing Lot Size and Harvest Size | |
Implicit Differentiation and Related Rates | |
Cumulative Review for Chapters 1–3 | |
Exponential and Logarithmic Functions | |
Exponential Functions | |
Logarithmic Functions | |
Differentiation of Logarithmic and Exponential Functions | |
Two Applications to Economics: Relative Rates and Elasticity of Demand | |
Integration and Its Applications | |
Antiderivatives and Indefinite Integrals | |
Integration Using Logarithmic and Exponential Functions | |
Definite Integrals and Areas | |
Further Applications of Definite Integrals: Average Value and Area Between Curves | |
Two Applications to Economics: Consumers' Surplus and Income Distribution | |
Integration by Substitution | |
Integration Techniques | |
Integration by Parts | |
Integration Using Tables | |
Improper Integrals | |
Numerical Integration | |
Calculus of Several Variables | |
Functions of Several Variables | |
Partial Derivatives | |
Optimizing Functions of Several Variables | |
Least Squares | |
Lagrange Multipliers and Constrained Optimization | |
Total Differentials and Approximate Changes | |
Multiple Integrals | |
Cumulative Review for Chapters 1–7 | |
Trigonometric Functions | |
Triangles, Angles, and Radian Measure | |
Sine and Cosine Functions | |
Derivatives of Sine and Cosine Functions | |
Integrals of Sine and Cosine Functions | |
Other Trigonometric Functions | |
Differential Equations | |
Separation of Variables | |
Further Applications of Differential Equations: Three Models of Growth | |
First–Order Linear Differential Equations | |
Approximate Solutions of Differential Equations: Euler's Method | |
Sequences and Series | |
Geometric Series | |
Taylor Polynomials | |
Taylor Series | |
Newton's Method | |
Probability | |
Discrete Probability | |
Continuous Probability | |
Uniform and Exponential Random Variables | |
Normal Random Variables | |
Cumulative Review for Chapters 1–11 | |
Appendix | |
Answers to Selected Exercises | |
Index | |
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