Linear Equations and Functions | |

Solutions of Linear Equations and Inequalities in One Variable | |

Equations | |

Linear Inequalities | |

Functions | |

Relations and Functions | |

Graphs of Functions | |

Function Notation | |

Domains and Ranges | |

Operations with Functions | |

Linear Functions | |

Intercepts | |

Rate of Change | |

Slope of a Line | |

Writing Equations of Lines | |

Solutions of Systems of Linear Equations | |

Graphical Solution | |

Solution by Substitution | |

Solution by Elimination | |

Three Equations in Three Variables | |

Applications of Functions in Business and Economics | |

Total Cost, Total Revenue, and Profit | |

Break-Even Analysis | |

Supply, Demand, and Market Equilibrium | |

Supply, Demand, and Taxation | |

Chapter Exercises | |

Quadratic and Other Special Functions | |

Quadratic Equations | |

Factoring Methods | |

The Quadratic Formula | |

Quadratic Functions: Parabolas | |

Parabolas | |

Business Applications of Quadratic Functions | |

Supply, Demand, and Market Equilibrium | |

Break-Even Points and Maximization | |

Special Functions and Their Graphs | |

Basic Functions | |

Polynomial and Rational Functions | |

Piecewise Defined Functions | |

Modeling Data with Graphing Utilities (optional) | |

Chapter Exercises | |

Chapter 3 Matrices | |

Operations with Matrices | |

Addition and Subtraction of Matrices | |

Scalar Multiplication | |

Multiplication of Matrices | |

Product of Two Matrices | |

Gauss-Jordan Elimination: Solving Systems of Equations | |

Systems with Unique Solutions | |

Systems with Nonunique Solutions | |

Nonsquare Systems | |

Inverse of a Square Matrix | |

Matrix Equations | |

Determinants | |

Chapter Exercises | |

Inequalities and Linear Programming | |

Linear Inequalities in Two Variables | |

One Linear Inequality in Two Variables | |

Systems of Linear Inequalities | |

Linear Programming: Graphical Methods | |

Solving Graphically | |

The Simplex Method: Maximization | |

The Simplex Method | |

Tasks and Procedure | |

Nonunique Solutions: Multiple Solutions and No Solution | |

The Simplex Method: Duality and Minimization | |

Dual Problems | |

Duality and Solving | |

The Simplex Method with Mixed Constraints | |

Mixed Constraints and Maximization | |

Mixed Constraints and Minimization | |

Chapter Exercises | |

Exponential and Logarithmic Functions | |

Exponential Functions | |

Modeling with Exponential Functions | |

Logarithmic Functions and Their Properties | |

Logarithmic Functions and Graphs | |

Modeling with Logarithmic Functions | |

Properties of Logarithms | |

Change of Base | |

Applications of Exponential and Logarithmic Functions | |

Solving Exponential Equations Using Logarithmic | |

Properties | |

Growth and Decay | |

Economic and Management Applications | |

Chapter Exercises | |

Mathematics of Finance | |

Simple Interest and Arithmetic Sequences | |

Future Value | |

Arithmetic Sequences | |

Compound Interest and Geometric Sequences | |

Compound IntereSt. Geometric Sequences | |

Future Values of Annuities | |

Ordinary Annuities | |

Annuities Due | |

Present Values of Annuities | |

Ordinary Annuities | |

Annuities Due | |

Deferred Annuities | |

Loans and Amortization | |

Amortization | |

Unpaid Balance of a Loan | |

Chapter Exercises | |

Introduction to Probability | |

Probability and Odds | |

Sample Spaces and Single Events | |

Empirical Probability | |

Odds | |

Unions, Intersections, and Complements of Events | |

Inclusion-Exclusion Principle | |

Conditional Probability: The Product Rule | |

Probability Trees and Bayes' Formula | |

Probability Trees | |

Bayes' Formula | |

Counting: Permutations and Combinations | |

Permutations | |

Combinations | |

Permutations, Combinations, and Probability | |

Chapter Exercises | |

Probability and Data Description | |

Binomial Probability Experiments | |

Describing Data | |

Statistical Graphs | |

Types of Averages | |

Variance and Standard Deviation | |

Discrete Probability Distributions | |

Discrete Probability Distributions | |

Measures of Dispersion | |

The Binomial Distribution | |

Binomial Formula | |

Normal Probability Distribution. z-Scores | |

Chapter Exercises | |

Derivatives | |

Limits | |

Notion of a Limit | |

Properties of Limits, Algebraic Evaluation | |

Limits of Piecewise Defined Functions | |

Continuous Functions | |

Limits at Infinity | |

Continuous Functions | |

Limits at Infinity | |

Average and Instantaneous Rates of Change: The Derivative | |

Instantaneous Rates of Change: Velocity | |

Tangent to a Curve | |

Differentiability and Continuity | |

Derivative Formulas | |

Additional Formulas | |

Marginal Revenue | |

The Product Rule and the Quotient Rule | |

Product Rule | |

Quotient Rule | |

The Chain Rule and the Power Rule | |

Chain Rule | |

Power Rule | |

Using Derivative Formulas | |

Higher-Order Derivatives | |

Second Derivatives | |

Higher-Order Derivatives | |

Derivatives in Business and Economics | |

Marginal Revenue | |

Marginal CoSt. Marginal Profit | |

Chapter Exercises | |

Applications of Derivatives | |

Relative Maxima and Minima: Curve Sketching | |

Concavity: Points of Inflection | |

Points of Inflection | |

Second-Derivative Test | |

Optimization in Business and Economics | |

Absolute Extrema | |

Maximizing Revenue | |

Minimizing Average CoSt. Maximizing Profit | |

Applications of Maxima and Minima | |

Rational Functions: More Curve Sketching | |

Asymptotes | |

More Curve Sketching | |

Chapter Exercises | |

Derivatives Continued | |

Derivatives of Logarithmic Functions | |

Using Properties of Logarithms | |

Derivatives of Exponential Functions | |

Implicit Differentiation | |

Related Rates | |

Percent Rates of Change | |

Solving Related-Rates Problems | |

Applications in Business and Economics | |

Elasticity of Demand | |

Taxation in a Competitive Market | |

Chapter Exercises | |

Indefinite Integrals | |

The Indefinite Integral | |

The Power Rule | |

Integrals Involving Exponential and Logarithmic Functions | |

Integrals Involving Exponential Functions | |

Integrals Involving Logarithmic Functions | |

The Indefinite Integral in Business and Economics | |

Total Cost and Profit | |

National Consumption and Savings | |

Differential Equations | |

Solution of Differential Equations | |

Separable Differential Equations | |

Applications of Differential Equations | |

Chapter Exercises | |

Definite Integrals: Techniques of Integration | |

The Definite Integral: The Fundamental Theorem of Calculus | |

Estimating the Area under a Curve | |

Area between Two Curves | |

Definite Integrals in Business and Economics | |

Continuous Income Streams | |

Consumer's Surplus | |

Producer's Surplus | |

Using Tables of Integrals | |

Integration by Parts | |

Improper Integrals and Their Applications | |

Chapter Exercises | |

Functions of Two or More Variables | |

Functions of Two or More Variables | |

Partial Differentiation | |

First-Order Partial Derivatives | |

Higher-Order Partial Derivatives | |

Functions of Two Variables in Business and Economics | |

Joint Cost and Marginal CoSt | |

Production Functions | |

Demand Functions | |

Maxima and Minima | |

Constrained Optimization and Lagrange Multipliers | |

Chapter Exercises | |

Answers to Odd-Numbered Exercises | |

Index | |

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