Description:
1. LINEAR FUNCTIONS AND MODELS. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Chapter Project: Modeling Spending on Internet Advertising. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions. 2. NONLINEAR MODELS. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Chapter Project: 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. 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. Chapter Project: Reducing Sulfur Emissions. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability. 4. TECHNIQUES OF DIFFERENTIATION. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Chapter Project: Projecting Market Growth. Optional Internet Topic: Linear Approximation and Error Estimation. 5. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates. Elasticity. Chapter Project: Production Lot Size Management. 6. THE INTEGRAL. 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. Chapter Project: Wage Inflation. Optional Internet Topic: Numerical Integration. 7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. Chapter Project: Estimating Tax Revenues. 8. FUNCTIONS OF SEVERAL VARIABLES. 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. Chapter Project: Modeling Household Income. 9. TRIGONOMETRIC MODELS. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications. Chapter Project: Predicting Cocoa Inventories. Appendix A: Algebra Review. OPTIONAL INTERNET CHAPTERS. S. CALCULUS APPLIED TO PROBABILITY AND STATISTICS. Continuous Random Variables and Histograms. Probability Density Functions: Uniform, Exponential, Normal, and Beta. Mean, Median, Variance and Standard Deviation. Chapter Project: Creating a Family Trust.
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