Description
Book SynopsisTable of ContentsI. A Library of Elementary Functions
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
