Finite Mathematics and Applied Calculus

Finite Mathematics and Applied Calculus
ISBN-10
0495019488
ISBN-13
9780495019480
Series
Finite Mathematics and Applied Calculus
Category
Calculus
Pages
1148
Language
English
Published
2007-02-01
Publisher
Thomson
Authors
Stefan Waner, Steven Costenoble

Description

1. FUNCTIONS AND LINEAR MODELS. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Chapter Project: Modeling Spending on Internet Advertising. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Two Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations. Chapter Project: The Impact of Regulating Sulfur Emissions. 3. MATRIX ALGEBRA AND APPLICATIONS. Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Input-Output Models. Chapter Project: The Japanese Economy. 4. LINEAR PROGRAMMING. 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). Chapter Project: Airline Scheduling. 5. THE MATHEMATICS OF FINANACE. Simple Interest. Compound Interest. Annuities, Loans, and Bonds. Chapter Project: Saving for College. 6. SETS AND COUNTING. Set Operations. Cardinality. The Addition and Multiplication Principles. Permutations and Combinations. Chapter Project: Designing a Puzzle. 7. PROBABILITY. Sample Spaces and Events. Estimated Probability. Empirical Probability. Probability and Counting Techniques. Probability Distributions. Conditional Probability and Independence. Bayes'' Theorem and Applications. Chapter Project: The Monty Hall Problem. 8. RANDOM VARIABLES AND STATISTICS. Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions. Chapter Project: Spotting Tax Fraud with Benford''s Law. Optional Internet Topics: Sampling Distributions and the Central Limit Theorem. Confidence Intervals. Hypothesis Testing. 9. MARKOV SYSTEMS. Markov Systems. Distribution Vectors and Powers of the Transition Matrix. Long-Range Behavior of Regular Markov Systems. Absorbing Markov Systems. Chapter Project: Predicting the Price of Gold. 10. NONLINEAR MODELS. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Chapter Project: 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. 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. Chapter Project: Reducing Sulfur Emissions. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability. 12. TECHNIQUES OF DIFFERENTIATION. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Chapter Project: Projecting Market Growth. Optional Internet Topic: Linear Approximation and Error Estimation. 13. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates. Elasticity. Chapter Project: Production Lot Size Management. 14. THE INTEGRAL. 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. Chapter Project: Wage Inflation. Optional Internet Topic: Numerical Integration. 15. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Continuous Income Streams. Improper Integrals and Applica

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