, APPLIED MATHEMATICS FOR THE MANAGERIAL,
LIFE, and SOCIAL SCIENCES
CONTENTS
CHAPTER 1 ‘FUNDAMENTALS OF ALGEBRA
Real Numbers
Polynomials
Factoring Polynomials
Rational Expressions
Integral Exponents
Solving Equations
Rational Exponents and Radicals
Quadratic Equations
=a
2 = Inequalities and
OOAONOOARWHND Absolute Value
Chapter 1 Review Exercises
CHAPTER 2 FUNCTIONS AND THEIR GRAPHS
2.1 The Cartesian Coordinate System and Straight Lines
2.2 Equations of Lines
2.3 Functions and Their Graphs
2.4 The Algebra of Functions
2.5 Linear Functions
2.6 Quadratic Functions
2.7 Functions and Mathematical Models
Chapter 2 Review Exercises
CHAPTER 3 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Exponential Functions as Mathematical Models
Chapter 3 Review Exercises
,CHAPTER4 MATHEMATICS OF FINANCE
4.1 Compound Interest 96
4.2 Annuities 101
4.3 Amortization and Sinking Funds 104
4.4 Arithmetic and Geometric Progressions - 110
Chapter 4 Review Exercises 113
‘
CHAPTER5 SYSTEMS OF LINEAR EQUATIONS AND MATRICES
5.1 Systems of Linear Equations--Introduction 116
5.2 Solving Systems of Linear Equations: Unique Solutions 120
5.3 Solving Systems of Linear Equations: Undetermined and
Overdetermined Systems| 131
5.4 Matrices 137
5.5 Multiplication of Matrices 142
5.6 The Inverse of a Square Matrix 148
Chapter 5 Review Exercises 160
CHAPTER 6 LINEAR PROGRAMMING
6.1 Graphing Systems of Linear Inequalities in Two Variables 168
6.2 Linear Programming Problems 173
6.3 Graphical Solution of Linear Programming Problems 179
6.4 The Simplex Method: Standard Maximization Problems 193
6.5 The Simplex Method: Standard Minimization Problems 215
Chapter 6 Review Exercises 232
CHAPTER7 SETS AND PROBABILITY
7.1 Sets and Set Operations 241
7.2 The Number of Elements in a Finite Set 245
7.3 The Multiplication Principle 250
7.4 Permutations and Combinations 251
7.5 Experiments, Sample Spaces, and Events 256
7.6 Probability 258
7.7 Rules of Probability ‘ 261
Chapter 7 Review Exercises 264
, CHAPTER 8 ADDITIONAL TOPICS IN PROBABILITY
Use of Counting Techniques in Probability 269
Conditional Probability and Independent Events 273
Bayes' Theorem 279
Distributions of Random Variables 286
Expected Value
Variance and Standard Deviation 292
Chapter 8 Review Exercises 295
CHAPTER9 THE DERIVATIVE
Limits
Continuity
The Derivative
Basic Rules of Differentiation
The Product and Quotient Rules; Higher-Order Derivatives
The Chain Rule
Differentiation of Exponential and Logarithmic Functions
Marginal Functions in Economics
Chapter 9 Review Exercises
CHAPTER 10 APPLICATIONS OF THE DERIVATIVE
10.1 Applications of the First Derivative 363
10.2 Applications of the Second Derivative 374
10.3 Curve Sketching 385
10.4 Optimization | 401
10.5 Optimization II 413
Chapter 10 Review Exercises 419
CHAPTER 11. INTEGRATION
11.1 Antiderivatives and the Rules of Integration 432
Integration by Substitution 437
Area and the Definite Integral 443
The Fundamental Theorem of Calculus 446
Evaluating Definite Integrals 449
Area Between Two Curves 454
Applications of the Definite Integral to Business and
Economics 461
Chapter 11 Review Exercises 464
LIFE, and SOCIAL SCIENCES
CONTENTS
CHAPTER 1 ‘FUNDAMENTALS OF ALGEBRA
Real Numbers
Polynomials
Factoring Polynomials
Rational Expressions
Integral Exponents
Solving Equations
Rational Exponents and Radicals
Quadratic Equations
=a
2 = Inequalities and
OOAONOOARWHND Absolute Value
Chapter 1 Review Exercises
CHAPTER 2 FUNCTIONS AND THEIR GRAPHS
2.1 The Cartesian Coordinate System and Straight Lines
2.2 Equations of Lines
2.3 Functions and Their Graphs
2.4 The Algebra of Functions
2.5 Linear Functions
2.6 Quadratic Functions
2.7 Functions and Mathematical Models
Chapter 2 Review Exercises
CHAPTER 3 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Exponential Functions as Mathematical Models
Chapter 3 Review Exercises
,CHAPTER4 MATHEMATICS OF FINANCE
4.1 Compound Interest 96
4.2 Annuities 101
4.3 Amortization and Sinking Funds 104
4.4 Arithmetic and Geometric Progressions - 110
Chapter 4 Review Exercises 113
‘
CHAPTER5 SYSTEMS OF LINEAR EQUATIONS AND MATRICES
5.1 Systems of Linear Equations--Introduction 116
5.2 Solving Systems of Linear Equations: Unique Solutions 120
5.3 Solving Systems of Linear Equations: Undetermined and
Overdetermined Systems| 131
5.4 Matrices 137
5.5 Multiplication of Matrices 142
5.6 The Inverse of a Square Matrix 148
Chapter 5 Review Exercises 160
CHAPTER 6 LINEAR PROGRAMMING
6.1 Graphing Systems of Linear Inequalities in Two Variables 168
6.2 Linear Programming Problems 173
6.3 Graphical Solution of Linear Programming Problems 179
6.4 The Simplex Method: Standard Maximization Problems 193
6.5 The Simplex Method: Standard Minimization Problems 215
Chapter 6 Review Exercises 232
CHAPTER7 SETS AND PROBABILITY
7.1 Sets and Set Operations 241
7.2 The Number of Elements in a Finite Set 245
7.3 The Multiplication Principle 250
7.4 Permutations and Combinations 251
7.5 Experiments, Sample Spaces, and Events 256
7.6 Probability 258
7.7 Rules of Probability ‘ 261
Chapter 7 Review Exercises 264
, CHAPTER 8 ADDITIONAL TOPICS IN PROBABILITY
Use of Counting Techniques in Probability 269
Conditional Probability and Independent Events 273
Bayes' Theorem 279
Distributions of Random Variables 286
Expected Value
Variance and Standard Deviation 292
Chapter 8 Review Exercises 295
CHAPTER9 THE DERIVATIVE
Limits
Continuity
The Derivative
Basic Rules of Differentiation
The Product and Quotient Rules; Higher-Order Derivatives
The Chain Rule
Differentiation of Exponential and Logarithmic Functions
Marginal Functions in Economics
Chapter 9 Review Exercises
CHAPTER 10 APPLICATIONS OF THE DERIVATIVE
10.1 Applications of the First Derivative 363
10.2 Applications of the Second Derivative 374
10.3 Curve Sketching 385
10.4 Optimization | 401
10.5 Optimization II 413
Chapter 10 Review Exercises 419
CHAPTER 11. INTEGRATION
11.1 Antiderivatives and the Rules of Integration 432
Integration by Substitution 437
Area and the Definite Integral 443
The Fundamental Theorem of Calculus 446
Evaluating Definite Integrals 449
Area Between Two Curves 454
Applications of the Definite Integral to Business and
Economics 461
Chapter 11 Review Exercises 464
