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PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS.CHAPTER 1. A Beginning Library of Elementary Functions.
1-2 Elementary Functions: Graphs and Transformations.
1-3 Linear Functions and Straight Lines.
1-4 Quadratic Functions.
Group Activity 1: Introduction to Regression Analysis.
Group Activity 2: Mathematical Modeling in Business.CHAPTER 2. Additional Elementary Functions.
2-1 Polynomial and Rational Functions.
2-2 Exponential Functions.
2-3 Logarithmic Functions.
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions.
Group Activity 2: Comparing Regression Models.
PART TWO. FINITE MATHEMATICS.CHAPTER 3. Mathematics of Finance.
3-1 Simple Interest.
3-2 Compound Interest.
3-3 Future Value of an Annuity; Sinking Funds.
3-4 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.CHAPTER 4. Systems of Linear Equations; Matrices.
4-1 Review: Systems of Linear Equations in Two Variables.
4-2 Systems of Linear Equations and Augmented Matrices.
4-3 Gauss-Jordan Elimination.
4-4 Matrices: Basic Operations.
4-5 Inverse of a Square Matrix.
4-6 Matrix Equations and Systems of Linear Equations.
4-7 Leontief Input-Output Analysis.
Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit.
Group Activity 2: Direct and Indirect Operating Costs.CHAPTER 5. Linear Inequalities and Linear Programming.
5-1 Systems of Linear Inequalities in Two Variables.
5-2 Linear Programming in Two Dimensions—A Geometric Approach.
5-3 A Geometric Introduction to the Simplex Method.
5-4 The Simplex Method: Maximization with Problem Constraints of the Form =.
5-5 The Dual; Minimization with Problem Constraints of the Form =.
5-6 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.CHAPTER 6. Logic, Sets, and Counting.
6-3 Basic Counting Principles.
6-4 Permutations and Combinations.
Group Activity 1: Combinations with Repetition Allowed.
Group Activity 2: Subset Lattices of Finite Sets.CHAPTER 7. Probability.
7-1 Sample Spaces, Events, and Probability.
7-2 Union, Intersection, and Complement of Events; Odds.
7-3 Conditional Probability, Intersection, and Independence.
7-4 Bayes' Formula.
7-5 Random Variable, Probability Distribution, and Expected Value.
Group Activity 1: Car and Crying Towels.
Group Activity 2: Simulation—A Draft Lottery for Professional Sports.CHAPTER 8. Markov Chains.
8-1 Properties of Markov Chains.
8-2 Regular Markov Chains.
8-3 Absorbing Markov Chains.
Group Activity 1: Social Mobility.
Group Activity 2: Gambler's Ruin.
PART THREE. CALCULUS.CHAPTER 9. The Derivative.
9-1 Introduction to Limits.
9-2 Limits and Continuity.
9-3 The Derivative.
9-4 Derivative of Constants, Power Forms, and Sums.
9-5 Derivatives of Products and Quotients.
9-6 Chain Rule: Power Form.
9-7 Marginal Analysis in Business and Economics.
Group Activity 1: Minimal Average Cost.
Group Activity 2: Numerical Differentiation on a Graphing Utility.CHAPTER 10. Graphing and Optimization.
10-1 First Derivative and Graphs.
10-2 Second Derivative and Graphs.
10-3 Curve Sketching Techniques; Unified and Extended.
10-4 Optimization; Absolute Maxima and Minima.
Group Activity 1: Maximizing Profit.
Group Activity 2: Minimizing Construction Costs.CHAPTER 11. Additional Derivative Topics.
11-1 The Constant e and Continuous Compound Interest.
11-2 Derivatives of Logarithmic and Exponential Functions.
11-3 Chain Rule: General Form.
11-4 Implicit Differentiation.
11-5 Related Rates.
Group Activity 1: Elasticity of Demand.
Group Activity 2: Point of Diminishing Returns.CHAPTER 12. Integration.
12-1 Antiderivatives and Indefinite Integrals.
12-2 Integration by Substitution.
12-3 Differential Equations; Growth and Decay.
12-4 The Definite Integral.
12-5 The Fundamental Theorem of Calculus.
Group Activity 1: Simpson's Rule.
Group Activity 2: Bell-Shaped Curves.CHAPTER 13. Additional Integration Topics.
13-1 Area Between Curves.
13-2 Applications in Business and Economics.
13-3 Integration by Parts.
13-4 Integration Using Tables.
Group Activity 1: Analysis of Income Concentration from Raw Data.
Group Activity 2: Grain Exchange.CHAPTER 14. Multivariable Calculus.
14-1 Functions of Several Variables.
14-2 Partial Derivatives.
14-3 Maxima and Minima.
14-4 Maxima and Minima Using Lagrange Multipliers.
14-5 Method of Least Squares.
14-6 Double Integrals Over Rectangular Regions.
Group Activity 1: City Planning.
Group Activity 2: Numerical Integration of Multivariable Functions.APPENDIX A. Basic Algebra Review.
B-1 Sequences, Series, and Summation Notation.APPENDIX C. Tables.