College mathematics : for business, economics, life sciences, and social sciences

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Front Cover Title Page Copyright Page Contents Preface Diagnostic Prerequisite Test Chapter 1 Functions and Graphs 1.1 Functions 1.2 Elementary Functions: Graphs and Transformations 1.3 Quadratic Functions 1.4 Polynomial and Rational Functions 1.5 Exponential Functions 1.6 Logarithmic Functions Chapter 1 Summary and Review Review Exercises Chapter 2 Mathematics of Finance 2.1 Simple Interest 2.2 Compound and Continuous Compound Interest 2.3 Future Value of an Annuity; Sinking Funds 2.4 Present Value of an Annuity; Amortization Chapter 2 Summary and Review Review Exercises Chapter 3 Systems of Linear Equations; Matrices 3.1 Review: Systems of Linear Equations in Two Variables 3.2 Systems of Linear Equations and Augmented Matrices 3.3 Gauss–Jordan Elimination 3.4 Matrices: Basic Operations 3.5 Inverse of a Square Matrix 3.6 Matrix Equations and Systems of Linear Equations 3.7 Leontief Input–Output Analysis Chapter 3 Summary and Review Review Exercises Chapter 4 Linear Inequalities and Linear Programming 4.1 Linear Inequalities in Two Variables 4.2 Systems of Linear Inequalities in Two Variables 4.3 Linear Programming in Two Dimensions: a Geometric Approach Chapter 4 Summary and Review Review Exercises Chapter 5 Linear Programming: The Simplex Method 5.1 The Table Method: an Introduction to the Simplex Method 5.2 The Simplex Method: Maximization with Problem Constraints of the Form … 5.3 The Dual Problem: Minimization with Problem Constraints of the Form ú 5.4 Maximization and Minimization with Mixed Problem Constraints Chapter 5 Summary and Review Review Exercises Chapter 6 Logic, Sets, and Counting 6.1 Logic 6.2 Sets 6.3 Basic Counting Principles 6.4 Permutations and Combinations Chapter 6 Summary and Review Review Exercises Chapter 7 Probability 7.1 Sample Spaces, Events, and Probability 7.2 Union, Intersection, and Complement of Events; Odds 7.3 Conditional Probability, Intersection, and Independence 7.4 Bayes’ Formula 7.5 Random Variable, Probability Distribution, and Expected Value Chapter 7 Summary and Review Review Exercises Chapter 8 Limits and the Derivative 8.1 Introduction to Limits 8.2 Infinite Limits and Limits at Infinity 8.3 Continuity 8.4 The Derivative 8.5 Basic Differentiation Properties 8.6 Differentials 8.7 Marginal Analysis in Business and Economics Chapter 8 Summary and Review Review Exercises Chapter 9 Additional Derivative Topics 9.1 The Constant E and Continuous Compound Interest 9.2 Derivatives of Exponential and Logarithmic Functions 9.3 Derivatives of Products and Quotients 9.4 The Chain Rule 9.5 Implicit Differentiation 9.6 Related Rates 9.7 Elasticity of Demand Chapter 9 Summary and Review Review Exercises Chapter 10 Graphing and Optimization 10.1 First Derivative and Graphs 10.2 Second Derivative and Graphs 10.3 L’hôpital’s Rule 10.4 Curve-Sketching Techniques 10.5 Absolute Maxima and Minima 10.6 Optimization Chapter 10 Summary and Review Review Exercises Chapter 11 Integration 11.1 Antiderivatives and Indefinite Integrals 11.2 Integration by Substitution 11.3 Differential Equations; Growth and Decay 11.4 The Definite Integral 11.5 The Fundamental Theorem of Calculus 11.6 Area Between Curves Chapter 11 Summary and Review Review Exercises Chapter 12 Additional Integration Topics 12.1 Integration by Parts 12.2 Other Integration Methods 12.3 Applications in Business and Economics Chapter 12 Summary and Review Review Exercises Chapter 13 Multivariable Calculus 13.1 Functions of Several Variables 13.2 Partial Derivatives 13.3 Maxima and Minima 13.4 Maxima and Minima Using Lagrange Multipliers 13.5 Method of Least Squares 13.6 Double Integrals over Rectangular Regions 13.7 Double Integrals over More General Regions Chapter 13 Summary and Review Review Exercises Chapter 14 Markov Chains 14.1 Properties of Markov Chains 14.2 Regular Markov Chains 14.3 Absorbing Markov Chains Chapter 14 Summary and Review Review Exercises Appebdix A Linear Equations and Graphs A.1 Linear Equations and Inequalities A.2 Graphs and Lines A.3 Linear Regression Appendix B Basic Algebra Review B.1 Real Numbers B.2 Operations on Polynomials B.3 Factoring Polynomials B.4 Operations on Rational Expressions B.5 Integer Exponents and Scientific Notation B.6 Rational Exponents and Radicals B.7 Quadratic Equations Appendix C Special Topics C.1 Sequences, Series, and Summation Notation C.2 Arithmetic and Geometric Sequences C.3 Binomial Theorem C.4 Interpolating Polynomials and Divided Differences Appendix D Integration Formulas Answers Index Index of Applications Back Cover