Applied Calculus (with InfoTrac) Book

1. LINEAR FUNCTIONS AND MODELS. Introduction. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Case Study: Modeling Spending on Internet Advertising. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions.
2.NONLINEAR MODELS. Introduction. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Case Study: Checking up on Malthus. Optional Internet Topics: Inverse Functions. Linear and Exponential Regression. Using and Deriving Algebraic Properties of Logarithms.
3.INTRODUCTION TO THE DERIVATIVE. Introduction. Average Rate of Change. The Derivative: Numerical and Graphical Viewpoints. The Derivative : Algebraic Viewpoint. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. Limits: Numerical and Graphical Approaches. Limits and Continuity. Limits and Continuity: Algebraic Approach. Case Study: Reducing Sulfur Emissions. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability.
4.TECHNIQUES OF DIFFERENTIATION. Introduction. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Case Study: Projecting Market Growth. Optional Internet Topic: Linear Approximation and Error Estimation.
5.APPLICATIONS OF THE DERIVATIVE. Introduction. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates.Elasticity. Case Study: Production Lot Size Management.
6.THE INTEGRAL. Introduction. The Indefinite Integral. Substitution. The Definite Integral as a Sum: A Numerical Approach. The Definite Integral as Area: A Geometric Approach. The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus. Case Study: Wage Inflation. Optional Internet Topic: Numerical Integration.
7.FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Introduction. Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. Case Study: Estimating Tax Revenues.
8.FUNCTIONS OF SEVERAL VARIABLES. Introduction. Functions of Several Variables from the Numerical and Algebraic Viewpoints. Three Dimensional Space and the Graph of a Function of Two Variables. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals. Case Study: Modeling Household Income.
9.TRIGONOMETRIC MODELS. Introduction. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications. Case Study: Predicting Cocoa Inventories.

Appendix A: Algebra Review. Introduction. Real Numbers. Exponents and Radicals. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. OPTIONAL INTERNET

ChapterS. S. Calculus Applied to Probability and Statistics. Introduction. Continuous Random Variables and Histograms. Probability Density Functions: Uniform, Exponential, Normal, and Beta. Mean, Median, Variance and Standard Deviation. Case Study: Creating a Family Trust.