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