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

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