Table of Contents
R. Functions, Graphs, and Models.
R.1 Graphs and Equations.
R.2 Functions and Models.
R.3 Finding Domain and Range.
R.4 Slope and Linear Functions.
R.5 Nonlinear Functions and Models.
R.6 Mathematical Modeling and Curve Fitting.
Extended Technology Application: Payrolls of Professional Basketball Teams
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits of Difference Quotients.
1.5 Differentiation Techniques: The Power and Sum-Difference Rules.
1.6 Differentiation Techniques: The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives.
Extended Technology Application: Path of a Baseball: The Tale of the Tape.
2. Applications of Differentiation.
2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs.
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs.
2.3 Graph Sketching: Asymptotes and Rational Functions.
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values.
2.5 Maximum-Minimum Problems: Business and Economics Applications.
2.6 Marginals and Differentials.
2.7 Implicit Differentiation and Related Rates.
Extended Technology Application: Maximum Sustainable Harvest
3. Exponential and Logarithmic Functions.
3.1 Exponential Functions.
3.2 Logarithmic Functions.
3.3 Applications: The Uninhibited Growth Model, dP/dt = kP.
3.4 Applications: Decay.
3.5 The Derivatives of a x and logax.
3.6 An Economics Application: Elasticity of Demand.
Extended Technology Application: The Business of Motion Picture Box-Office Revenue.
4.1 The Area Under a Graph
4.2 Area, Antiderivatives, and Integrals.
4.3 Area and Definite Integrals.
4.4 Properties of Definite Integrals.
4.5 Integration Techniques: Substitution.
4.6 Integration Techniques: Integration by Parts.
4.7 Integration Techniques: Tables.
Extended Technology Application: Financial Predictions for Starbucks, Lowes, The Gap, and Intel
5. Applications of Integration.
5.1 An Economics Application: Consumer Surplus and Producer Surplus.
5.2 Applications of the Models
5.3 Improper Integrals.
5.5 Probability: Expected Value; The Normal Distribution.
5.7 Differential Equations.
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda.
6. Functions of Several Variables.
6.1 Functions of Several Variables.
6.2 Partial Derivatives.
6.3 Maximum-Minimum Problems.
6.4 An Application: The Least-Squares Technique.
6.5 Constrained Maximum and Minimum Values: Lagrange Multipliers.
6.6 Double Integrals
Extended Technology Application: Minimizing Employees' Travel Time in a Building.
Appendix A: Review of Basic Algebra.
Areas for a Standard Normal Distribution.
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