Mathematics
Finite Mathematics and Applied Calculus, 2nd Edition
ISBN-10: 061837213X ISBN-13: 9780618372133
1200 Pages Casebound
© 2005 Published
- Overview
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- About the Author
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- Table of Contents
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- Features
Table of Contents
Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.
1. Functions
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1.1 Real Numbers, Inequalities, and Lines
1.2 Exponents
1.3 Functions
1.4 Functions, Continued
1.5 Exponential Functions
1.6 Logarithmic Functions
I. Finite Mathematics
2. Mathematics of Finance
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2.1 Simple Interest
2.2 Compound Interest
2.3 Annuities
2.4 Amortization
3. Systems of Equations and Matrices
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3.1 Systems of Two Linear Equations in Two Variables
3.2 Matrices and Linear Equations in Two Variables
3.3 Systems of Linear Equations and the Gauss-Jordan Method
3.4 Matrix Arithmetic
3.5 Inverse Matrices and Systems of Linear Equations
3.6 Introduction to Modeling: Leontief Models and Least Squares
4. Linear Programming
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4.1 Linear Inequalities
4.2 Two-Variable Linear Programming Problems
4.3 The Simplex Method for Standard Maximum Problems
4.4 Standard Minimum Problems and Duality
4.5* Nonstandard Problems: The Dual Pivot Element and the Two-Stage Method
4.6* Nonstandard Problems: Artificial Variables and the Big-M Method
* These two sections provide alternate methods for solving the same types of problems. The choice of which to cover is left to the Instructor.
5. Probability
Application Preview: The Chevalier de Meré
5.1 Sets, Counting, and Venn Diagrams
5.2 Permutations and Combinations
5.3 Probability Spaces
5.4 Conditional Probability and Independence
5.5 Bayes' Formula
5.6 Random Variables and Distributions
6. Statistics
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6.1 Random Samples and Data Organization
6.2 Measures of Central Tendency
6.3 Measures of Variation
6.4 Normal Distributions and Binomial Approximation
7. Markov Chains
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7.1 States and Transitions
7.2 Regular Markov Chains
7.3 Absorbing Markov Chains
II. Calculus
8. Derivatives and Their Uses
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8.1 Limits and Continuity
8.2 Rates of Change, Slopes, and Derivatives
8.3 Some Differentiation Formulas
8.4 The Product and Quotient Rules
8.5 Higher-Order Derivatives
8.6 The Chain Rule and Generalized Power Rule
8.7 Nondifferentiable Functions
9. Further Applications of Derivatives
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9.1 Graphing Using the First Derivative
9.2 Graphing Using the First and Second Derivatives
9.3 Optimization
9.4 Further Applications of Optimization
9.5 Optimizing Lot Size and Harvest Size
9.6 Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1, 8-9
10. Exponential and Logarithmic Functions
Application Preview: Elasticity and Social Policy
10.1 Review of Exponential and Logarithmic Functions
10.2 Differentiation of Logarithmic and Exponential Functions
10.3 Two Applications to Economics: Related Rates and Elasticity of Demand
11. Integration and Its Applications
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11.1 Antiderivatives and Indefinite Integrals
11.2 Integration Using Logarithmic and Exponential Functions
11.3 Definite Integrals and Areas
11.4 Further Applications of Definite Integrals: Average Value and Area Between Curves
11.5 Two Applications to Economics: Consumers' Surplus and Income Distribution
11.6 Integration by Substitution
12. Integration Techniques and Differential Equations
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12.1 Integration by Parts
12.2 Integration Using Tables
12.3 Improper Integrals
12.4 Numerical Integration
12.5 Differential Equations
12.6 Further Applications of Differential Equations: Three Models of Growth
13. Calculus of Several Variables
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13.1 Functions of Several Variables
13.2 Partial Derivatives
13.3 Optimizing Functions of Several Variables
13.4 Least Squares
13.5 Lagrange Multipliers and Constrained Optimization
13.6 Total Differentials and Approximate Changes
13.7 Multiple Integrals
Cumulative Review for Chapters 1, 8-13
Appendix: Normal Probabilities Using Tables
Answers to Selected Exercises
Index
Available on the Web
G. Game Theory
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G.1 Two-Person Games and Saddle Points
G.2 Mixed Strategies
G.3 Games and Linear Programming
Chapter L Logic
L.1 Statements and Connectives
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L.2 Truth Tables
Application Preview: Circuits
L.3 Implications
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L.4 Valid Arguments
Application Preview: Fuzzy Logic and Artificial Intelligence
L.5 Quantifiers and Euler Diagrams
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Chapter Projects and Essays