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Finite Mathematics and Applied Calculus With Infotrac,9780534419677
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Finite Mathematics and Applied Calculus With Infotrac

by
Edition:
3rd
ISBN13:

9780534419677

ISBN10:
0534419674
Format:
Paperback
Pub. Date:
7/21/2003
Publisher(s):
Brooks Cole
List Price: $156.00

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What version or edition is this?
This is the 3rd edition with a publication date of 7/21/2003.
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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.

Summary

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

Table of Contents

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 APPLICATIONS
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: Designing a Puzzle
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 INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL
Introduction
Integration by Parts
Area Between Two Curves and Applications
Averages and Moving Averages
Continuous Income Streams
Improper Integrals and Applications
Differential Equations and Applications
Case Study: Estimating Tax Revenues
16. FUNCTIONS OF SEVERAL VARIABLES
Introduction
Functions of Several Variables from the Numerical and Algebraic Viewpoints
Three Dimensional Space and the Graph of a Function of Two Variables
Partial Derivatives
Maxima and Minima
Constrained Maxima and Minima and Applications
Double Integrals
Case Study: Modeling Household Income
17. TRIGONOMETRIC MODELS
Introduction
Trigonometric Functions, Models, and Regression
Derivatives of Trigonometric Functions and Applications
Integrals of Trigonometric Functions and Applications
Case Study: Predicting Cocoa Inventories
Appendix A: Algebra Review
Introduction
Real Numbers
Exponents and Radicals
Multiplying and Factoring Algebraic Equations
Rational Expressions
Solving Polynomial Equations
Solving Miscellaneous Equations
OPTIONAL INTERNET CHAPTERS
G
Game Theory
Introduction
Two-Person Zero Sum Games; Reduction by Dominance
Strictly Determined Games
Solving Games using the Simplex Method
Expert Opinion--Harvesting Forests
L
Introduction to Logic
Introduction
Statements and Logical Operators
Logical Equivalence, Tautologies and Contradictions
The Conditional and the Biconditional
Tautological Implications and Tautological Equivalences
Rules of Inference
Arguments and Proofs
S
Calculus Applied to Probability and Statistics
Introduction
Continuous Random Variables and Histograms
Probability Density Functions: Uniform, Exponential, Normal, and Beta
Mean, Median, Variance and Standard Deviation
Case Study: Creating a Family Trust
Appendix A: Real Numbers
Appendix B: Table: Area Under a Normal Curve
Answers to Selected Exercises


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