Brief Applied Calculus Book

1. FUNCTIONS AND MODELS. Functions and their Representations. Combining and Transforming Functions. Linear Models and Rates of Change. Polynomial Models and Power Functions. Exponential Models. Logarithmic Functions. 2. THE DERIVATIVE. Measuring Change. Limits. Rates of Change and Derivatives. The Derivative as a Function. 3. TECHNIQUES OF DIFFERENTIATION. Short Cuts to Finding Derivatives. Introduction to Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation and Logarithms. Exponential Growth and Decay. 4. APPLICATIONS OF DIFFERENTIATION. Related Rates. Maximum and Minimum Values. Derivatives and the Shapes of Curves. Asymptotes. Curve Sketching. Optimization. Optimization in Business and Economics. 5. INTEGRALS. Cost, Area, and the Definite Integral. Fundamental Theorem of Calculus. The Net Change Theorem and Average Value. The Substitution Rule. Integration by Parts. 6. APPLICATIONS OF INTEGRATION. Areas Between Curves. Applications to Economics. Applications to Biology. Differential Equations. Improper Integrals. Probability. 7. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maximum and Minimum Values. LaGrange Multipliers.