Applied Calculus, Brief Book

Preface. A User's Guide to Features. Integrating Excel. Graphing Calculator Terminology. 1. FUNCTIONS. Real Numbers, Inequalities, and Lines. Exponents. Functions. Functions, Continued. 2. 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. 3. FURTHER APPLICATIONS OF DERIVATIVES. Graphing Using the First Derivative. Graphing Using the and Second Derivatives. Optimization. Further Applications of Optimization. Optimizing Lot Size and Harvest Size. Implicit Differentiation and Related Rules. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Differentiation of Logarithmic and Exponential Functions. Two Applications to Economics: Relative Rates and Elasticity of Demand. 5. 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. 6. INTEGRATION TECHNIQUES AND DIFFERENTIAL EQUATIONS. Integration by Parts. Integration Using Tables. Improper Integrals. Numerical Integration. Differential Equations. Further Applications of Differential Equations: Three Models of Growth. 7. 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. Answers to Selected Exercises. Index.