Preface 

ix  
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS 

1  (126) 

Chapter 1 A Beginning Library of Elementary Functions 


3  (74) 


3  (20) 

12 Elementary Functions: Graphs and Transformations 


23  (13) 

13 Linear Functions and Straight Lines 


36  (16) 


52  (15) 

Important Terms and Symbols 


67  (1) 


68  (4) 

Group Activity 1: Introduction to Regression Analysis 


72  (2) 

Group Activity 2: Mathematical Modeling in Business 


74  (3) 

Chapter 2 Additional Elementary Functions 


77  (50) 

21 Polynomial and Rational Functions 


77  (16) 

22 Exponential Functions 


93  (14) 

23 Logarithmic Functions 


107  (13) 

Important Terms and Symbols 


120  (1) 


120  (3) 

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions 


123  (1) 

Group Activity 2: Comparing Regression Models 


124  (3) 
PART TWO FINITE MATHEMATICS 

127  (384) 

Chapter 3 Mathematics of Finance 


129  (46) 


129  (6) 


135  (14) 

33 Future Value of an Annuity; Sinking Funds 


149  (7) 

34 Present Value of an Annuity; Amortization 


156  (12) 

Important Terms and Symbols 


168  (1) 


168  (3) 

Group Activity 1: Reducing Interest Payments on a Home Mortgage 


171  (1) 

Group Activity 2: Yield to Maturity and Internal Rate of Return 


172  (3) 

Chapter 4 Systems of Linear Equations: Matrices 


175  (90) 

41 Review: Systems of Linear Equations in Two Variables 


176  (13) 

42 Systems of Linear Equations and Augmented Matrices 


189  (10) 

43 GaussJordan Elimination 


199  (15) 

44 Matrices: Basic Operations 


214  (13) 

45 Inverse of a Square Matrix 


227  (12) 

46 Matrix Equations and Systems of Linear Equations 


239  (11) 

47 Leontief InputOutput Analysis 


250  (8) 

Important Terms and Symbols 


258  (1) 


259  (3) 

Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit 


262  (1) 

Group Activity 2: Direct and Indirect Operating Costs 


263  (2) 

Chapter 5 Linear Inequalities and Linear Programming 


265  (100) 

51 Systems of Linear Inequalities in Two Variables 


265  (14) 

52 Linear Programming in Two DimensionsA Geometric Approach 


279  (15) 

53 A Geometric Introduction to the Simplex Method 


294  (8) 

54 The Simplex Method: Maximization with Problem Constraints of the Form less than or equal to 


302  (20) 

55 The Dual; Minimization with Problem Constraints of the Form greater than or equal to 


322  (17) 

56 Maximization and Minimization with Mixed Problem Constraints 


339  (19) 

Important Terms and Symbols 


358  (1) 


359  (2) 

Group Activity 1: The TwoPhase Method (An Alternative to the Big M Method) 


361  (3) 

Group Activity 2: Production Scheduling 


364  (1) 


365  (98) 

61 Basic Counting Principles 


366  (10) 

62 Permutations and Combinations 


376  (13) 

63 Sample Spaces, Events, and Probability 


389  (16) 

64 Union, Intersection, and Complement of Events; Odds 


405  (15) 

65 Conditional Probability, Intersection, and Independence 


420  (16) 


436  (7) 

67 Random Variable, Probability Distribution, and Expected Value 


443  (10) 

Important Terms and Symbols 


453  (1) 


454  (5) 

Group Activity 1: Car and Crying Towels 


459  (1) 

Group Activity 2: SimulationA Draft Lottery for Professional Sports 


460  (3) 


463  (48) 

71 Properties of Markov Chains 


463  (13) 

72 Regular Markov Chains 


476  (12) 

73 Absorbing Markov Chains 


488  (16) 

Important Terms and Symbols 


504  (1) 


504  (4) 

Group Activity 1: Social Mobility 


508  (1) 

Group Activity 2: Gambler's Ruin 


509  (2) 
PART THREE CALCULUS 

511  (432) 


513  (92) 

81 Rate of Change and Slope 


514  (13) 


527  (17) 


544  (13) 

84 Derivatives of Constants, Power Forms, and Sums 


557  (13) 

85 Derivatives of Products and Quotients 


570  (8) 

86 Chain Rule: Power Form 


578  (8) 

87 Marginal Analysis in Business and Economics 


586  (11) 

Important Terms and Symbols 


597  (1) 

Summary of Rules of Differentiation 


598  (1) 


598  (5) 

Group Activity 1: Minimal Average Cost 


603  (1) 

Group Activity 2: Numerical Differentiation on a Graphing Utility 


604  (1) 

Chapter 9 Graphing and Optimization 


605  (90) 

91 Continuity and Graphs 


606  (16) 

92 First Derivative and Graphs 


622  (17) 

93 Second Derivative and Graphs 


639  (16) 

94 Curve Sketching Techniques: Unified and Extended 


655  (16) 

95 Optimization; Absolute Maxima and Minima 


671  (16) 

Important Terms and Symbols 


687  (1) 


688  (4) 

Group Activity 1: Maximizing Profit 


692  (1) 

Group Activity 2: Minimizing Construction Costs 


692  (3) 

Chapter 10 Additional Derivative Topics 


695  (50) 

101 The Constant e and Continuous Compound Interest 


695  (8) 

102 Derivatives of Logarithmic and Exponential Functions 


703  (12) 

103 Chain Rule: General Form 


715  (12) 

104 Implicit Differentiation 


727  (7) 


734  (6) 

Important Terms and Symbols 


740  (1) 

Additional Rules of Differentiation 


740  (1) 


741  (2) 

Group Activity 1: Elasticity of Demand 


743  (1) 

Group Activity 2: Point of Diminishing Returns 


744  (1) 


745  (84) 

111 Antiderivatives and Indefinite Integrals 


745  (15) 

112 Integration by Substitution 


760  (12) 

113 Differential EquationsGrowth and Decay 


772  (12) 

114 A GeometricNumeric Introduction to the Definite Integral 


784  (16) 

115 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus 


800  (19) 

Important Terms and Symbols 


819  (1) 

Integration Formulas and Properties 


819  (1) 


819  (5) 

Group Activity 1: Simpson's Rule 


824  (3) 

Group Activity 2: BellShaped Curves 


827  (2) 

Chapter 12 Additional Integration Topics 


829  (46) 


829  (12) 

122 Applications in Business and Economics 


841  (13) 

123 Integration by Parts 


854  (7) 

124 Integration Using Tables 


861  (8) 

Important Terms and Symbols 


869  (1) 


869  (2) 

Group Activity 1: Analysis of Income Concentration from Raw Data 


871  (2) 

Group Activity 2: Grain Exchange 


873  (2) 

Chapter 13 Multivariable Calculus 


875  (68) 

131 Functions of Several Variables 


875  (10) 


885  (10) 


895  (9) 

134 Maxima and Minima Using Lagrange Multipliers 


904  (10) 

135 Method of Least Squares 


914  (11) 

136 Double Integrals Over Rectangular Regions 


925  (11) 

Important Terms and Symbols 


936  (1) 


936  (3) 

Group Activity 1: City Planning 


939  (1) 

Group Activity 2: Numerical Integration of Multivariable Functions 


940  (3) 

Appendix A Basic Algebra Review 


943  (68) 

SelfTest on Basic Algebra 


943  (2) 


945  (6) 

A2 Algebra and Real Numbers 


951  (7) 

A3 Operations on Polynomials 


958  (7) 

A4 Factoring Polynomials 


965  (6) 

A5 Operations on Rational Expressions 


971  (7) 

A6 Integer Exponents and Scientific Notation 


978  (6) 

A7 Rational Exponents and Radicals 


984  (7) 

A8 Linear Equations and Inequalities in One Variable 


991  (10) 


1001  (10) 

Appendix B Special Topics 


1011  (18) 

B1 Sequences, Series, and Summation Notation 


1011  (6) 

B2 Arithmetic and Geometric Sequences 


1017  (8) 


1025  (4) 


1029  

Table I Basic Geometric Formulas 


1029  (2) 

Table II Integration Formulas 


1031  
Answers 

A1  
Index 

I1  
Library of Elementary Functions 

Inside front cover  
Applications Index 

Inside back cover  