(NOTE: Each chapter includes a list of Important Terms and Symbols and Review Exercises.)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.
II. TWO FINITE MATHEMATICS.
3. Mathematics of Finance.
Simple Interest. Compound Interest. Future Value of an Annuity; Sinking Funds. Present Value of an Annuity; Amortization. Group Activity 1: Reducing Interest Payments on a Home Mortgage. Group Activity 2: Yield to Maturity and Internal Rate of Return.
4. Systems of Linear Equations; Matrices.
Review: Systems of Linear Equations in Two Variables. Systems of Linear Equations and Augmented Matrices. Gauss-Jordan Elimination. Matrices: Basic Operations. Inverse of a Square Matrix. Matrix Equations and Systems of Linear Equations. Leontief Input-Output Analysis. Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit. Group Activity 2: Direct and Indirect Operating Costs.
5. Linear Inequalities and Linear Programming.
Systems of Linear Inequalities in Two Variables. Linear Programming in Two Dimensions-A Geometric Approach. A Geometric Introduction to the Simplex Method. The Simplex Method: Maximization with Problem Constraints of the Form d". The Dual; Minimization with Problem Constraints of the Form e". Maximization and Minimization with Mixed Problem Constraints. Group Activity 1: The Two-Phase Method (An Alternative to the Big M Method). Group Activity 2: Production Scheduling.
6. Probability.
Basic Counting Principles. Permutations and Combinations. Sample Spaces, Events, and Probability. Union, Intersection, and Complement of Events; Odds. Conditional Probability, Intersection, and Independence. Bayes' Formula. Random Variable, Probability Distribution, and Expected Value. Group Activity 1: Car and Crying Towels. Group Activity 2: Simulation-A Draft Lottery for Professional Sports.
7. Markov Chains.
Properties of Markov Chains. Regular Markov Chains. Absorbing Markov Chains. Group Activity 1: Social Mobility. Group Activity 2: Gambler's Ruin.
III. THREE CALCULUS.
8. The Derivative.
Introduction to Limits. Limits and Continuity. 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.
9. Graphing and Optimization.
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.
10. 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.
11. Integration.
Antiderivatives and Indefinite Integrals. Integration by Substitution. Differential Equations-Growth and Decay. A 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.
12. 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.
13. 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.
14. Differential Equations.
Basic Concepts. Separation of Variables. First-Order Linear Differential Equations. Group Activity 1: Torricelli's Law. Group Activity 2: Euler's Method.
15. 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.
APPENDICES.
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.
C. Tables.
Basic Geometric Formulas. Integration Formulas. Area Under the Standard Normal Curve.
Answers.
Index.
Library of Elementary Functions.
Applications Index.
