I. A LIBRARY OF ELEMENTARY FUNCTIONS.
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.
Introduction to Limits. Limits and Continuity. The Derivative. Derivative of Constants, Power Forms, and Sums. Derivatives of Products and Quotients. Chain Rule: Power Form. Marginal Analysis in Business & Economics. Group Activity 1: Minimal Average Cost. Group Activity 2: Numerical Differentiation on a Graphing Utility.
4. Graphing and Optimization.
First Derivative and Graphs. Second Derivative and Graphs. Curve Sketching Techniques: Unified & 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. Group Activity 1: Elasticity of Demand. Group Activity 2: Point of Diminishing Returns.
Antiderivative 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. Differential Equations.
Basic Concepts. Separation of Variables. First-Order Linear Differential Equations. Group Activity 1: Torricelli's Law. Group Activity 2: Euler's Method.
10. Taylor Polynomials and Infinite Series.
Taylor Polynomials. Taylor Series. Operations on Taylor Series. Approximations Using Taylor Series. Group Activity 1: L'Hopital's Rule. Group Activity 2: Taylor Series Solutions to Differential Equations.
11. Probability and Calculus.
Improper Integrals. Continuous Random Variables. Expected Value, Standard Deviation, and Median. Special Probability Distributions. Group Activity 1: Beta Distributions. Group Activity 2: Chi-Square Distributions.
12. 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.
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.
B. Special Topics.
Sequences, Series, and Summation Notation. Arithmetic and Geometric Sequences. The Binomial Theorem. Increments and Differentials. L'Hopital's Rule. Double Integrals Over More General Regions. Interpolating Polynomials and Divided Differences.
Basic Geometric Formulas. Integration Formulas. Area Under the Standard Normal Curve.
Library of Elementary Functions.