1. A Beginning Library of Elementary Functions.
Functions. Elementary Functions: Graphs and Transformations. Linear Functions and Straight Lines. Quadratic Functions. Group Activity 1: Introduction to Regression Analysis. Group Activity 2: Mathematical Modeling in Business. 2. Additional Elementary Functions.
Polynomial and Rational Functions. Exponential Functions. Logarithmic Functions. Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions. Group Activity 2: Comparing Regression Models.
3. The Derivative.
Rate of Change and Slope. Limits. The Derivative. Derivatives of Constants, Power Forms, and Sums. Derivatives of Products and Quotients. Chain Rule: Power Form. Marginal Analysis in Business and Economics. Summary of Rules of Differentiation. Group Activity 1: Minimal Average Cost. Group Activity 2: Numerical Differentiation on a Graphing Utility. 4. Graphing and Optimization.
Continuity and Graphs. First Derivative and Graphs. Second Derivative and Graphs. Curve Sketching Techniques: Unified and Extended. Optimization; Absolute Maxima and Minima. Group Activity 1: Maximizing Profit. Group Activity 2: Minimizing Construction Costs. 5. Additional Derivative Topics.
The Constant e and Continuous Compound Interest. Derivatives of Logarithmic and Exponential Functions. Chain Rule: General Form. Implicit Differentiation. Related Rates. Additional Rules of Differentiation. Group Activity 1: Elasticity of Demand. Group Activity 2: Point of Diminishing Returns. 6. Integration.
Antiderivatives and Indefinite Integrals. Integration by Substitution. Differential Equations; Growth and Decay. Geometric-Numeric Introduction to the Definite Integral. Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus. Integration Formulas and Properties. Group Activity 1: Simpson's Rule. Group Activity 2: Bell-Shaped Curves. 7. Additional Integration Topics.
Area Between Curves. Applications in Business and Economics. Integration by Parts. Integration Using Tables. Group Activity 1: Analysis of Income Concentration from Raw Data. Group Activity 2: Grain Exchange. 8. Multivariable Calculus.
Functions of Several Variables. Partial Derivatives. Maxima and Minima. Maxima and Minima Using Lagrange Multipliers. Method of Least Squares. Double Integrals over Rectangular Regions. Group Activity 1: City Planning. Group Activity 2: Numerical Integration of Multivariable Functions. 9. Trigonometric Functions.
Trigonometric Functions Review. Derivatives of Trigonometric Functions. Integration of Trigonometric Functions. Group Activity 1: Seasonal Business Cycles. Group Activity 2: Heating Degree Days. Appendix A. Basic Algebra Review.
Self-Test on Basic Algebra. Sets. Algebra and Real Numbers. Operations on Polynomials. Factoring Polynomials. Operations on Rational Expressions. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Linear Equations and Inequalities in One Variable. Quadratic Equations. Appendix B. Special Topics.
Sequences, Series, and Summation Notation. Arithmetic and Geometric Sequences. The Binomial Theorem. Appendix C. Tables.
Geometric Formulas. Integration Formulas. Answers. Index. Library of Elementary Functions. Application Index.