Finite Mathematics and Calculus Applied to the Real World

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Finite Mathematics and Calculus Applied to the Real World

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Finite Mathematics
Applied to the Real World

Calculus
Applied to the Real World

Chapter 1 Functions and Graphs
Introduction
1.1 Coordinates and Graphs
1.2 Functions and their Graphs
1.3 Linear Functions
1.4 Linear Models
1.5 Quadratic Functions and Models
1.6 Solving Equations Using Graphing Calculators or Computers
You're the Expert--Modeling the Demand for Poultry
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Additional On-Line Topics
New Functions from Old: Scaled and Shifted Functions
Fitting Functions to Data: Regression

Math Tools for Chapter 1
Java Graphing Utility | Function Evaluator & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 2 Systems of Linear Equations and Matrices
Introduction
2.1 Systems of Two Linear Equations in Two Unknowns
2.2 Using Matrices to Solve Systems with Two Unknowns On-line tutorial for Section 2.2
2.3 Using Matrices to Solve Systems with Three or More Unknowns On-line tutorial for Section 2.3
2.4 Applications of Systems of Linear Equations
You're the Expert--The Impact of Regulating Sulfur Emissions
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Math Tools for Chapter 2
Row Operation and Pivoting Utility | Graphing Calculator Pivot Program (TI-82/83) | Free Mac Gauss-Jordan Program


Chapter 3 Matrix Algebra
Introduction
3.1 Matrix Addition and Scalar Multiplication
3.2 Matrix Multiplication
3.3 Matrix Inversion
3.4 Input-Output Models
You're the Expert--The Japanese Economy
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Math Tools for Chapter 3
Matrix Algebra Tool | Free Mac Matrix Algebra Program


Chapter 4 Linear Programming
Introduction
4.1 Graphing Linear Inequalities
4.2 Solving Linear Programming Problems Graphically
4.3 Solving Standard Linear Programming Problems using the Simplex Method On-line tutorial for Section 4.3
4.4 Solving Nonstandard Linear Programming Problems
You're the Expert --Airline Scheduling
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Math Tools for Chapter 4
Simplex Method Tool | Row Operation and Pivoting Utility | Graphing Calculator Pivot Program (TI-82/83) | Free Mac Pivot Program


Chapter 5 Sets and Counting
Introduction
5.1 Sets
5.2 The Number of Elements in a Set
5.3 The Multiplication Principle; Permutations
5.4 The Addition Principle; Combinations
You're the Expert--Designing a Puzzle
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises


Chapter 6 Probability
Introduction
6.1 Sample Spaces and Events On-line tutorial for Section 6.1
6.2 Introduction to Probability On-line tutorial for Section 6.2
6.3 Principles of Probability On-line tutorial for Section 6.3
6.4 Counting Techniques and Probability
6.5 Conditional Probability and Independence On-line tutorial for Section 6.5
6.6 Bayes' Theorem and Applications On-line tutorial for Section 6.6
6.7 Bernoulli Trials Probability Distribution Generator and Grapher for Bernoulli Trials
You're the Expert--The Monty Hall Problem On-line Monty Hall Simulation (Java)
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Math Tools for Chapter 6
Probability Distribution Generator and Grapher for Bernoulli Trials


Chapter 7 Statistics
Introduction
7.1 Random Variables and Distributions
7.2 Mean, Median, and Mode
7.3 Variance and Standard Deviation
7.4 Normal Distributions
You're the Expert--Lies, Damned Lies, and Statistics
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises
On-Line Chapter on Calculus & Statistics

Additional On-Line Topics
Sampling Distributions & Central Limit Theorem
Fitting Functions to Data: Regression

Math Tools for Chapter 7
Histogram and Probability Distribution Generator | Probability Distribution Generator and Grapher for Bernoulli Trials


Chapter 8 Mathematics of Finance
Introduction
8.1 Simple Interest
8.2 Compound Interest
8.3 Annuities and Loans
You're the Expert--Pricing Auto Loans
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz


Chapter 9 Exponential and Logarithmic Functions
Introduction
9.1 Exponential Functions and Applications
9.2 Continuous Growth and Decay and the Number e
9.3 Logarithmic Functions
9.4 Applications of Logarithms
You're the Expert--Epidemics
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Math Tools for Chapter 9
Java Graphing Utility | Function Evaluator & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 10 Introduction to the Derivative
Introduction
10.1 Rates of Change and the Derivative On-line tutorial for Section 10.1
10.2 Geometric Interpretation of the Derivative On-line tutorial for Section 10.2
10.3 Limits and Continuity On-line tutorial for Section 10.3
10.4 Derivatives of Powers and Polynomials On-line tutorial for Section 10.4
10.5 Marginal Analysis
10.6 More on Limits, Continuity and Differentiability
You're the Expert--Reducing Sulfur Emissions
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Additional On-Line Topics
Sketching the Graph of the Derivative
Proof of the Power Rule

Math Tools for Chapter 10
Java Graphing Utility | Function Evaluator & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 11 Techniques of Differentiation
Introduction
11.1 The Product and Quotient Rules On-line tutorial for Section 11.1
11.2 The Chain Rule On-line tutorial for Section 11.2
11.3 Derivatives of Logarithmic and Exponential Functions On-line tutorial for Section 11.3
11.4 Implicit Differentiation
11.5 Linear Approximation and Error Estimation
You're the Expert --Estimating Mortgage Rates
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Additional On-Line Topics
Proof of the Quotient Rule
Proof of the Chain Rule
Proofs of some Trigonometric Limits


Chapter 12 Applications of the Derivative
Introduction
12.1 Maxima and Minima
12.2 Applications of Maxima and Minima
12.3 The Second Derivative: Acceleration and Concavity
12.4 Curve Sketching
12.5 Related Rates On-line tutorial for Section 12.5
12.6 Elasticity of Demand
You're the Expert--Production Lot Size Management
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Review Exercises on Maxima & Minima
On-Line Review Exercises onElasticity of Demand

Math Tools for Chapter 12
Java Graphing Utility | Function Evaluator & Grapher | Free Mac Grapher


Chapter 13 The Integral
Introduction
13.1 The Indefinite Integral On-line tutorial for Section 13.1
13.2 Substitution On-line tutorial for Section 13.2
13.3 Applications of the Indefinite Integral
13.4 Geometric Definition of the Definite Integral
13.5 Algebraic Definition of the Definite Integral
13.6 The Fundamental Theorem of Calculus
13.7 Numerical Integration
You're the Expert--The Cost of Issuing a Warranty
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Review Exercises for Chapter 13

Math Tools for Chapter 10
Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration


Chapter 14 Further Techniques and Applications of the Integral
Introduction
14.1 Integration by Parts
14.2 Integration Using Tables
14.3 Area Between Two Curves and Applications
14.4 Averages and Moving Averages
14.5 Improper Integrals and Applications
You're the Expert--Estimating Tax Revenues
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz


Chapter 15 Functions of Several Variables
Introduction
15.1 Functions of Two or More Variables
15.2 Three Dimensional Space and the Graph of a Function of Two Variables
15.3 Partial Derivatives
15.4 Maxima and Minima
15.5 Constrained Maxima and Minima Applications
5.6 Least Squares Fit Also See On-Line Material on Regression
You're the Expert--Constructing a Best Fit Demand Curve
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Math Tools for Chapter 15
Linear Multiple Regression Utility


On-Line Chapter: Introduction to Logic
(Text and Complete Exercise Sets On-Line)
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


On-Line Chapter: Calculus and Probability
(Text and Complete Exercise Sets On-Line)
Introduction
Continuous Random Variables and Histograms
Probability Density Functions: Uniform, Exponential, Normal, and Beta
Mean, Median, Variance and Standard Deviation
You're the Expert--Creating a Family Trust


On-Line Chapter: Trigonometric Functions and Calculus
(Text and Complete Exercise Sets On-Line)
Introduction
Modeling with the Sine Function
The Six Trigonometric Functions
Derivatives of Trigonometric Functions
Integrals of Trigonometric Functions


Appendix A: Algebra Review
Introduction
Operations on the Real Numbers On-line tutorial for Section A.1
Integer Exponents On-line tutorial for Section A.2
Radicals and Rational Exponents On-line tutorial for Section A.3
The Distributive Law: Multiplying Algebraic Expressions On-line tutorial for Section A.4
Factoring Algebraic Expressions On-line tutorial for Section A.5
Rational Expressions On-line tutorial for Section A.6
Equations On-line tutorial for Section A.7
Solving Polynomial Equations
Solving Miscellaneous Equations


Appendix B: Using a Graphing Calculator


Appendix C: Using a Computer Spreadsheet


Appendix D: A Table of Integrals


Appendix E: Table: Area Under a Normal Curve

Last Updated: April, 1998
Copyright © 1995-1996 HarperCollins Publishers
On-Line Materials Copyright © 1997-1998 Stefan Waner & Steven R. Costenoble