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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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