I. A Library of Elementary Functions

• 1. Linear Equations and Graphs
  • 1.1 Linear Equations and Inequalities
  • 1.2 Graphs and Lines
  • 1.3 Linear Regression
  • Chapter 1 Summary and Review
  • Review Exercises
• 2. Functions and Graphs
  • 2.1 Functions
  • 2.2 Elementary Functions: Graphs and Transformations
  • 2.3 Quadratic Functions
  • 2.4 Polynomial and Rational Functions
  • 2.5 Exponential Functions
  • 2.6 Logarithmic Functions
  • Chapter 2 Summary and Review
  • Review Exercises

II. Finite Mathematics

• 3. Mathematics of Finance
  • 3.1 Simple Interest
  • 3.2 Compound and Continuous Compound Interest
  • 3.3 Future Value of an Annuity; Sinking Funds
  • 3.4 Present Value of an Annuity; Amortization
  • Chapter 3 Summary and Review
  • Review Exercises
• 4. Systems of Linear Equations; Matrices
  • 4.1 Review: Systems of Linear Equations in Two Variables
  • 4.2 Systems of Linear Equations and Augmented Matrices
  • 4.3 Gauss – Jordan Elimination
  • 4.4 Matrices: Basic Operations
  • 4.5 Inverse of a Square Matrix
  • 4.6 Matrix Equations and Systems of Linear Equations
  • 4.7 Leontief Input – Output Analysis
  • Chapter 4 Summary and Review
  • Review Exercises
• 5. Linear Inequalities and Linear Programming
  • 5.1 Linear Inequalities in Two Variables
  • 5.2 Systems of Linear Inequalities in Two Variables
  • 5.3 Linear Programming in Two Dimensions: A Geometric Approach
  • Chapter 5 Summary and Review
  • Review Exercises
• 6. Linear Programming: The Simplex Method
  • 6.1 The Table Method: An Introduction to the Simplex Method
  • 6.2 The Simplex Method: Maximization with Problem Constraints of the Form ≤
  • 6.3 The Dual Problem: Minimization with Problem Constraints of the Form ≥
  • 6.4 Maximization and Minimization with Mixed Problem Constraints
  • Chapter 6 Summary and Review
  • Review Exercises
• 7. Logic, Sets, and Counting
  • 7.1 Logic
  • 7.2 Sets
  • 7.3 Basic Counting Principles
  • 7.4 Permutations and Combinations
  • Chapter 7 Summary and Review
  • Review Exercises
• 8. Probability
  • 8.1 Sample Spaces, Events, and Probability
  • 8.2 Union, Intersection, and Complement of Events; Odds
  • 8.3 Conditional Probability, Intersection, and Independence
  • 8.4 Bayes’ Formula
  • 8.5 Random Variable, Probability Distribution, and Expected Value
  • Chapter 8 Summary and Review
  • Review Exercises

III. Calculus

• 9. Limits and the Derivative
  • 9.1 Introduction to Limits
  • 9.2 Infinite Limits and Limits at Infinity
  • 9.3 Continuity
  • 9.4 The Derivative
  • 9.5 Basic Differentiation Properties
  • 9.6 Differentials
  • 9.7 Marginal Analysis in Business and Economics
  • Chapter 9 Summary and Review
  • Review Exercises
• 10. Additional Derivative Topics
  • 10.1 The Constant e and Continuous Compound Interest
  • 10.2 Derivatives of Exponential and Logarithmic Functions
  • 10.3 Derivatives of Products and Quotients
  • 10.4 The Chain Rule
  • 10.5 Implicit Differentiation
  • 10.6 Related Rates
  • 10.7 Elasticity of Demand
  • Chapter 10 Summary and Review
  • Review Exercises
• 11. Graphing and Optimization
  • 11.1 First Derivative and Graphs
  • 11.2 Second Derivative and Graphs
  • 11.3 L’Hôpital’s Rule
  • 11.4 Curve-Sketching Techniques
  • 11.5 Absolute Maxima and Minima
  • 11.6 Optimization
  • Chapter 11 Summary and Review
  • Review Exercises
• 12. Integration
  • 12.1 Antiderivatives and Indefinite Integrals
  • 12.2 Integration by Substitution
  • 12.3 Differential Equations; Growth and Decay
  • 12.4 The Definite Integral
  • 12.5 The Fundamental Theorem of Calculus
  • Chapter 12 Summary and Review
  • Review Exercises
• 13. Additional Integration Topics
  • 13.1 Area Between Curves
  • 13.2 Applications in Business and Economics
  • 13.3 Integration by Parts
  • 13.4 Other Integration Methods
  • Chapter 13 Summary and Review
  • Review Exercises
• 14. Multivariable Calculus
  • 14.1 Functions of Several Variables
  • 14.2 Partial Derivatives
  • 14.3 Maxima and Minima
  • 14.4 Maxima and Minima Using Lagrange Multipliers
  • 14.5 Method of Least Squares
  • 14.6 Double Integrals over Rectangular Regions
  • 14.7 Double Integrals over More General Regions
  • Chapter 14 Summary and Review
  • Review Exercises
• 15. Markov Chains (online at goo.gl/8SZkyn)
  • 15.1 Properties of Markov Chains
  • 15.2 Regular Markov Chains
  • 15.3 Absorbing Markov Chains
  • Chapter 15 Summary and Review
  • Review Exercises

Appendix A: Basic Algebra Review

• A.1 Real Numbers
• A.2 Operations on Polynomials
• A.3 Factoring Polynomials
• A.4 Operations on Rational Expressions
• A.5 Integer Exponents and Scientific Notation
• A.6 Rational Exponents and Radicals
• A.7 Quadratic Equations

Appendix B: Special Topics (online at goo.gl/mjbXrG)

• B.1 Sequences, Series, and Summation Notation
• B.2 Arithmetic and Geometric Sequences
• B.3 Binomial Theorem
• B.4 Interpolating Polynomials and Divided Differences

Appendix C: Tables

• Table I Integration Formulas
• Table II Area under the Standard Normal Curve

Answers

Index

Index of Applications