| |
| |
| Preface | |
| |
| |
| A Library of Elementary Functions | |
| |
| |
| A Beginning Library of Elementary Functions | |
| |
| |
| Functions | |
| |
| |
| Elementary Functions: Graphs and Transformations | |
| |
| |
| Linear Functions and Straight Lines | |
| |
| |
| Quadratic Functions | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Introduction to Regression Analysis | |
| |
| |
| Mathematical Modeling in Business | |
| |
| |
| Additional Elementary Functions | |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| Exponential Functions | |
| |
| |
| Logarithmic Functions | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions | |
| |
| |
| Comparing Regression Models | |
| |
| |
| Finite Mathematics | |
| |
| |
| Mathematics of Finance | |
| |
| |
| Simple Interest | |
| |
| |
| Compound Interest | |
| |
| |
| Future Value of an Annuity; Sinking Funds | |
| |
| |
| Present Value of an Annuity; Amortization | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Reducing Interest Payments on a Home Mortgage | |
| |
| |
| Yield to Maturity and Internal Rate of Return | |
| |
| |
| Systems of Linear Equations; Matrices | |
| |
| |
| Review: Systems of Linear Equations in Two Variables | |
| |
| |
| Systems of Linear Equations and Augmented Matrices | |
| |
| |
| Gauss-Jordan Elimination | |
| |
| |
| Matrices: Basic Operations | |
| |
| |
| Inverse of a Square Matrix | |
| |
| |
| Matrix Equations and Systems of Linear Equations | |
| |
| |
| Leontief Input-Output Analysis | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Using Matrices to Find Cost, Revenue, and Profit | |
| |
| |
| Direct and Indirect Operating Costs | |
| |
| |
| Linear Inequalities and Linear Programming | |
| |
| |
| Systems of Linear Inequalities in Two Variables | |
| |
| |
| Linear Programming in Two Dimensions--A Geometric Approach | |
| |
| |
| A Geometric Introduction to the Simplex Method | |
| |
| |
| The Simplex Method: Maximization with Problem Constraints of the Form [less than or equal] | |
| |
| |
| The Dual; Minimization with Problem Constraints of the Form [great than or equal] | |
| |
| |
| Maximization and Minimization with Mixed Problem Constraints | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| The Two-Phase Method (An Alternative to the Big M Method) | |
| |
| |
| Production Scheduling | |
| |
| |
| Probability | |
| |
| |
| Basic Counting Principles | |
| |
| |
| Permutations and Combinations | |
| |
| |
| Sample Spaces, Events, and Probability | |
| |
| |
| Union, Intersection, and Complement of Events; Odds | |
| |
| |
| Conditional Probability, Intersection, and Independence | |
| |
| |
| Bayes' Formula | |
| |
| |
| Random Variable, Probability Distribution, and Expected Value | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Car and Crying Towels | |
| |
| |
| Simulation--A Draft Lottery for Professional Sports | |
| |
| |
| Markov Chains | |
| |
| |
| Properties of Markov Chains | |
| |
| |
| Regular Markov Chains | |
| |
| |
| Absorbing Markov Chains | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Social Mobility | |
| |
| |
| Gambler's Ruin | |
| |
| |
| Calculus | |
| |
| |
| The Derivative | |
| |
| |
| Rate of Change and Slope | |
| |
| |
| Limits | |
| |
| |
| The Derivative | |
| |
| |
| Derivatives of Constants, Power Forms, and Sums | |
| |
| |
| Derivatives of Products and Quotients | |
| |
| |
| Chain Rule: Power Form | |
| |
| |
| Marginal Analysis in Business and Economics | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Summary of Rules of Differentiation | |
| |
| |
| Review Exercise | |
| |
| |
| Minimal Average Cost | |
| |
| |
| Numerical Differentiation on a Graphing Utility | |
| |
| |
| Graphing and Optimization | |
| |
| |
| Continuity and Graphs | |
| |
| |
| First Derivative and Graphs | |
| |
| |
| Second Derivative and Graphs | |
| |
| |
| Curve Sketching Techniques: Unified and Extended | |
| |
| |
| Optimization; Absolute Maxima and Minima | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Maximizing Profit | |
| |
| |
| Minimizing Construction Costs | |
| |
| |
| Additional Derivative Topics | |
| |
| |
| The Constant e and Continuous Compound Interest | |
| |
| |
| Derivatives of Logarithmic and Exponential Functions | |
| |
| |
| Chain Rule: General Form | |
| |
| |
| Implicit Differentiation | |
| |
| |
| Related Rates | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Additional Rules of Differentiation | |
| |
| |
| Review Exercise | |
| |
| |
| Elasticity of Demand | |
| |
| |
| Point of Diminishing Returns | |
| |
| |
| Integration | |
| |
| |
| Antiderivatives and Indefinite Integrals | |
| |
| |
| Integration by Substitution | |
| |
| |
| Differential Equations--Growth and Decay | |
| |
| |
| A Geometric-Numeric Introduction to the Definite Integral | |
| |
| |
| Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Integration Formulas and Properties | |
| |
| |
| Review Exercise | |
| |
| |
| Simpson's Rule | |
| |
| |
| Bell-Shaped Curves | |
| |
| |
| Additional Integration Topics | |
| |
| |
| Area between Curves | |
| |
| |
| Applications in Business and Economics | |
| |
| |
| Integration by Parts | |
| |
| |
| Integration Using Tables | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Analysis of Income Concentration from Raw Data | |
| |
| |
| Grain Exchange | |
| |
| |
| Multivariable Calculus | |
| |
| |
| Functions of Several Variables | |
| |
| |
| Partial Derivatives | |
| |
| |
| Maxima and Minima | |
| |
| |
| Maxima and Minima Using Lagrange Multipliers | |
| |
| |
| Method of Least Squares | |
| |
| |
| Double Integrals Over Rectangular Regions | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| City Planning | |
| |
| |
| Numerical Integration of Multivariable Functions | |
| |
| |
| Differential Equations | |
| |
| |
| Basic Concepts | |
| |
| |
| Separation of Variables | |
| |
| |
| First-Order Linear Differential Equations | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Torricelli's Law | |
| |
| |
| Euler's Method | |
| |
| |
| Probability and Calculus | |
| |
| |
| Improper Integrals | |
| |
| |
| Continuous Random Variables | |
| |
| |
| Expected Value, Standard Deviation, and Median | |
| |
| |
| Special Probability Distributions | |
| |
| |
| Important Terms and Symbols | |
| |
| |
| Review Exercise | |
| |
| |
| Beta Distributions | |
| |
| |
| Chi-Square Distributions | |
| |
| |
| Special Topics | |
| |
| |
| Sequences, Series, and Summation Notation | |
| |
| |
| Arithmetic and Geometric Sequences | |
| |
| |
| The Binomial Theorem | |
| |
| |
| Increments and Differentials | |
| |
| |
| L'Hopital's Rule | |
| |
| |
| Double Integrals Over More General Regions | |
| |
| |
| Tables 1085 | |
| |
| |
| Basic Geometric Formulas | |
| |
| |
| Integration Formulas | |
| |
| |
| Area Under the Standard Normal Curve | |
| |
| |
| Answers | |
| |
| |
| Index | |
| |
| |
| Library of Elementary Functions | |
| |
| |
| Applications Index | |