# Finite Mathematics and Calculus Applied to the Real World

## Table Of Contents & On-Line Resources for Finite Mathematics and Calculus Applied to the Real World

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 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