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PART 1 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 Review Review Exercise 2 Functions and Graphs 2-1 Functions 2-2 Elementary Functions: Graphs and Transformations 2-3 Quadratic Functions 2-4 Exponential Functions 2-5 Logarithmic Functions Chapter 2 Review Review Exercise PART 2 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 Review Review Exercise 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 2 Review Review Exercise 5 Linear Inequalities and Linear Programming 5-1 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 Review Review Exercise 6 Linear Programming: Simplex Method 6-1 A Geometric 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 Review Review Exercise 7 Logic, Sets, and Counting 7-1 Logic 7-2 Sets 7-3 Basic Counting Principles 7-4 Permutations and Combinations Chapter 7 Review Review Exercise 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 Review Review Exercise 9 Markov Chains 9-1 Properties of Markov Chains 9-2 Regular Markov Chains 9-3 Absorbing Markov Chains Chapter 9 Review Review Exercise PART 3 CALCULUS 10 Limits and the Derivative 10-1 Introduction to Limits 10-2 Continuity 10-3 Infinite Limits and Limits at Infinity 10-4 The Derivative 10-5 Basic Differentiation Properties 10-6 Differentials 10-7 Marginal Analysis in Business and Economics Chapter 10 Review Review Exercise 11 Additional Derivative Topics 11-1 The Constant e and Continuous Compound Interest 11-2 Derivatives of Exponential and Logarithmic Functions 11-3 Derivatives of Products and Quotients 11-4 The Chain Rule 11-5 Implicit Differentiation 11-6 Related Rates 11-7 Elasticity of Demand Chapter 11 Review Review Exercise 12 Graphing and Optimization 12-1 First Derivative and Graphs 12-2 Second Derivative and Graphs 12-3 L’Hôpital’s Rule 12-4 Curve-Sketching Techniques 12-5 Absolute Maxima and Minima 12-6 Optimization Chapter 12 Review Review Exercise 13 Integration 13-1 Antiderivatives and Indefinite Integrals 13-2 Integration by Substitution 13-3 Differential Equations; Growth and Decay 13-4 The Definite Integral 13-5 The Fundamental Theorem of Calculus Chapter 13 Review Review Exercise 14 Additional Integration Topics 14-1 Area between Curves 14-2 Applications in Business and Economics 14-3 Integration by Parts 14-4 Integration Using Tables Chapter 14 Review Review Exercise 15 Multivariable Calculus 15-1 Functions of Several Variables 15-2 Partial Derivatives 15-3 Maxima and Minima 15-4 Maxima and Minima Using Lagrange Multipliers 15-5 Method of Least Squares 15-6 Double Integrals over Rectangular Regions 15-7 Double Integrals over More General Regions Chapter 15 Review Review Exercise A Basic Algebra Review Self-Test on Basic Algebra A-1 Algebra and 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 B Special Topics B-1 Sequences, Series, and Summation Notation B-2 Arithmetic and Geometric Sequences B-3 The Binomial Theorem C Tables Table I Basic Geometric Formulas Table II Integration Formulas Answers Index Applications Index A Library of Elementary Functions Table of Contents
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