Mathematics with Applications for the Management, Life, and Social Sciences

PrefaceOne Set Theory 1.1 Introduction to Sets 1.2 Union and Intersection of Sets 1.3 Complementation and Cartesian Product of Sets Key Ideas for ReviewTwo Coordinate Systems and Graphs 2.1 Coordinate Systems 2.2 The Straight Line 2.3 Linear Systems of Two Equations in Two Unknowns 2.4 Applications of Linear Equations 2.5 Linear Inequalities and Their Graphs Key Ideas for ReviewThree Linear Programming (A Geometric Approach) 3.1 What Is Linear Programming? 3.2 Solving Linear Programming Problems Geometrically Key Ideas for ReviewFour Matrices and Linear Systems 4.1 Linear Systems 4.2 Gauss-Jordan Elimination 4.3 Matrices; Matrix Addition and Scalar Multiplication 4.4 Matrix Multiplication 4.5 Inverses of Matrices Key Ideas for ReviewFive Linear Programming (An Algebraic Approach) 5.1 Introduction; Slack Variables 5.2 The Key Ideas of the Simplex Method 5.3 The Simplex Method 5.4 Nonstandard Linear Programming Problems; Duality Key Ideas for ReviewSix Counting Techniques; Permutations and Combinations 6.1 Counting Elements in Sets 6.2 Permutations and Combinations Key Ideas for ReviewSeven Probability 7.1 Introduction; Sample Space and Events 7.2 Probability Models for Finite Sample Spaces 7.3 Basic Theorems of Probability 7.4 Solving Probability Problems 7.5 Conditional Probability; Independence 7.6 Bayes' Formula Key Ideas for ReviewEight Statistics 8.1 Introduction; Random Variables 8.2 Expected Value of a Random Variable 8.3 Variance of a Random Variable 8.4 Chebyshev's Inequality; Applications of Mean and Variance 8.5 Binomial Random Variables 8.6 The Normal Approximation of the Binomial 8.7 Hypothesis Testing; The Chi-Square Test Key Ideas for ReviewNine Applications 9.1 Applications of Probability and Expected Value to Life Insurance and Mortality 9.2 Introduction to Game Theory and Applications 9.3 Games with Mixed Strategies 9.4 An Application of Probability to Genetics; The Hardy-Weinberg Stability Principle 9.5 An Application of Conditional Probability to Medical Diagnosis 9.6 Markov Chains and Applications Key Ideas for ReviewTen Mathematics of Finance 10.1 Simple and Compound Interest 10.2 Effective Rate of Interest; Simple Discount 10.3 Annuities and Sinking Funds 10.4 Present Value 10.5 Mortgages and Amortization Schedules Key Ideas for ReviewEleven Functions, Limits, and Rates of Change 11.1 Introduction 11.2 Functions 11.3 Limits 11.4 Limits at Infinity 11.5 Continuity 11.6 Average and Instantaneous Rate of Change Key Ideas for ReviewTwelve The Derivative 12.1 The Derivative 12.2 The Chain Rule 12.3 Applications of the Derivative 12.4 Derivatives of the Exponential and Logarithmic Functions Key Ideas for ReviewThirteen Applications of Differentiation 13.1 Applications of Differentiation to Optimization 13.2 First and Second Derivative Tests 13.3 More Applications to Optimization 13.4 Sketching Graphs of Polynomial Functions 13.5 Applications to Exponential Growth and Decay Models Key Ideas for ReviewFourteen Integration 14.1 Antiderivatives and Indefinite Integrals 14.2 The Definite Integral 14.3 Properties of the Definite Integral 14.4 Techniques of Integration 14.5 Improper Integrals Key Ideas for ReviewFifteen Applications of Integration 15.1 Integrating Rates of Change 15.2 Differential Equations 15.3 Applications of Integration in Probability Key Ideas for ReviewSixteen Functions of Several Variables 16.1 Functions of Two Variables; Coordinate Systems in Three Dimensions 16.2 Partial Derivatives 16.3 Applications of Partial Derivatives to Optimization Key Ideas for ReviewAlgebra Review A.1 Real Numbers A.