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ISBN: 9780534419677 | 0534419674

Edition: 3rdFormat: Paperback

Publisher: Brooks Cole

Pub. Date: 7/21/2003

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1. FUNCTIONS AND LINEAR MODELS. Introduction. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Case Study: Modeling Spending on Internet Advertising. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Introduction. Systems of Two Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations. Case Study: The Impact of Regulating Sulfur Emissions. 3. MATRIX ALGEBRA AND APPLICA TIONS. Introduction. Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Input-Output Models. Case Study: The Japanese Economy. 4. LINEAR PROGRAMMING. Introduction. Graphing Linear Inequalities. Solving Linear Programming Problems Graphically. The Simplex Method: Solving Standard Maximization Problems. The Simplex Method: Solving General Linear Programming Problems. The Simplex Method and Duality (Optional). Case Study: Airline Scheduling. 5. THE MATHEMATICS OF FINANACE. Introduction. Simple Interest. Compound Interest. Annuities, Loans, and Bonds. Case Study: Saving for College. 6. SETS AND COUNTING. Introduction. Set Operations. Cardinality. The Addition and Multiplication Principles. Permutations and Combinations. Case Study: Designi ng a Puz zle. 7. PROBABILITY. Introduction. Sample Spaces and Events. Estimated Probability. Empirical Probability. Probability and Counting Techniques. Probability Distributions. Conditional Probability and Independence. Bayes'' Theorem and Applications. Case Study: The Monty Hall Problem. 8. RANDOM VARIABLES AND STATISTICS. Introduction. Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions. Case Study: Spotting Tax Fraud with Benford''s Law. Optional Internet Topics: Sampling Distributions and the Central Limit Theorem. Confidence Intervals. Hypothesis Testing. 9. MARKOV SYSTEMS. Introduction. Markov Systems. Distribution Vectors and Powers of the Transition Matrix. Long-Range Behavior of Regular Markov Systems. Absorbing Markov Systems. Case Study: Predicting the Price of Gold. 10. NONLINEAR MODELS. Introduction. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Case Study: Checking up on Malthus. Optional Internet Topics: Inverse Functions. Linear and Exponential Regression. Using and Deriving Algebraic Properties of Logarithms. 11. INTRODUCTION TO THE DERIVATIVE. Introduction. Average Rate of Change. The Derivative: Numerical and Graphical Viewpoints. The Derivative : Algebraic Viewpoint. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. Limits: Numerical and Graphical Approaches. Limits and Continuity. Limits and Continuity: Algebraic Approach. Case Study: Reducing Sulfur Emissions. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability. 12. TECHNIQUES OF DIFFERENTIATION. Introduction. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Case Study: Projecting Market Growth. Optional Internet Topic: Linear Approximation and Error Estimation. 13. APPLICATIONS OF THE DERIVATIVE. Introduction. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates. Elasticity. Case Study: Production Lot Size Management. 14. THE INTEGRAL. Introduction. The Indefinite Integral. Substitution. The Definite Integral as a Sum: A Numerical Approach. The Definite Integral as Area: A Geometric Approach. The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus. Case Study: Wage Inflation. Optional Internet Topic: Numerical Integration. 15. FURTHER