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Tables of Contents for Applied Mathematics for Business, Economics, Life Sciences, and Social Sciences
Chapter/Section Title
Page #
Page Count
Preface
xi
Part One A Library of Elementary Functions
1
128
A Beginning Library of Elementary Functions
3
76
Functions
3
20
Elementary Functions: Graphs and Transformations
23
13
Linear Functions and Straight Lines
36
17
Quadratic Functions
53
26
Important Terms and Symbols
68
1
Review Exercise
69
5
Group Activity 1: Introduction to Regression Analysis
74
1
Group Activity 2: Mathematical Modeling in Business
75
4
Additional Elementary Functions
79
50
Polynomial and Rational Functions
79
17
Exponential Functions
96
14
Logarithmic Functions
110
19
Important Terms and Symbols
122
1
Review Exercise
122
3
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions
125
1
Group Activity 2: Comparing Regression Models
125
4
Part Two Finite Mathematics
129
380
Mathematics of Finance
131
46
Simple Interest
132
6
Compound Interest
138
13
Future Value of an Annuity; Sinking Funds
151
8
Present Value of an Annuity; Amortization
159
18
Important Terms and Symbols
171
1
Review Exercise
171
3
Group Activity 1: Reducing Interest Payments on a Home Mortgage
174
1
Group Activity 2: Yield to Maturity and Internal Rate of Return
175
2
Systems of Linear Equations; Matrices
177
88
Review:Systems of Linear Equations in Two Variables
178
13
Systems of Linear Equations and Augmented Matrices
191
10
Gauss-Jordan Elimination
201
14
Matrices: Basic Operations
215
14
Inverse of a Square Matrix
229
11
Matrix Equations and Systems of Linear Equations
240
10
Leontief Input-Output Analysis
250
15
Important Terms and Symbols
258
1
Review Exercise
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
Linear Inequalities and Linear Programming
265
100
Systems of Linear Inequalities in Two Variables
265
15
Linear Programming in Two Dimensions: Geometric Approach
280
15
Geometric Introduction to the Simplex Method
295
8
The Simplex Method: Maximization with Problem Constraints of the Form ≤
303
19
Dual Problem: Minimization with Problem Constraints of the Form ≥
322
16
Maximization and Minimization with Mixed Problem Constraints
338
27
Important Terms and Symbols
357
1
Review Exercise
358
3
Group Activity 1: The Two-Phase Method (An Alternative to the Big M Method)
361
2
Group Activity 2: Production Scheduling
363
2
Probability
365
96
Basic Counting Principles
366
10
Permutations and Combinations
376
13
Sample Sapces, Events, and Probability
389
15
Union, Intersection, and Complement of Events; Odds
404
14
Conditional Probability, Intersection, and Independence
418
16
Bayes' Formula
434
7
Random Variable, Probability Distribution, and Expected Value
441
20
Important Terms and Symbols
451
1
Review Exercise
451
5
Group Activity 1: Car and Crying Towels
456
2
Group Activity 2: Simulation: Draft Lottery for Professional Sports
458
3
Markov Chains
461
48
Properties of Markov Chains
461
13
Regular Markov Chains
474
12
Absorbing Markov Chains
486
23
Important Terms and Symbols
501
1
Review Exercise
502
3
Group Activity 1: Social Mobility
505
1
Group Activity 2: Gambler's Ruin
506
3
Part Three Calculus
509
506
The Derivative
511
98
Introduction to Limits
512
16
Limits and Continuity
528
17
The Derivative
545
15
Derivatives of Constants, Power Forms, and Sums
560
14
Derivatives of Products and Quotients
574
8
Chain Rule: Power Form
582
7
Marginal Analysis in Business and Economics
589
20
Important Terms and Symbols
601
1
Summary of Rules of Differentiation
602
1
Review Exercise
602
5
Group Activity 1: Minimal Average Cost
607
1
Group Activity 2: Numerical Differentiation on a Graphing Utility
608
1
Graphing and Optimization
609
74
First Derivative and Graphs
610
17
Second Derivative and Graphs
627
16
Curve Sketching Techniques: Unified and Extended
643
17
Optimization; Absolute Maxima and Minima
660
23
Important Terms and Symbols
676
1
Review Exercise
676
4
Group Activity 1: Maximizing Profit
680
1
Group Activity 2: Minimizing Construction Costs
680
3
Additional Derivative Topics
683
48
The Constant e and Continuous Compound Interest
683
7
Derivatives of Logarithmic and Exponential Functions
690
12
Chain Rule: General Form
702
11
Implicit Differentiation
713
7
Related Rates
720
11
Important Terms and Symbols
726
1
Additional Rules of Differentiation
726
1
Review Exercise
726
2
Group Activity 1: Elasticity of Demand
728
1
Group Activity 2: Point of Diminishing Returns
729
2
Integration
731
82
Antiderivatives and Indefinite Integrals
731
15
Integration by Substitution
746
12
Differential Equations; Growth and Decay
758
11
Geometric-Numeric Introduction to the Definite Integral
769
16
Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus
785
28
Important Terms and Symbols
803
1
Integration Formulas and Properties
804
1
Review Exercise
804
4
Group Activity 1: Simpson's Rule
808
3
Group Activity 2: Bell-Shaped Curves
811
2
Additional Integration Topics
813
44
Area Between Curves
813
11
Applications in Business and Economics
824
13
Integration by Parts
837
8
Integration Using Tables
845
12
Important Terms and Symbols
852
1
Review Exercise
853
2
Group Activity 1: Analysis of Income Concentration from Raw Data
855
1
Group Activity 2: Grain Exchange
856
1
Multivariable Calculus
857
68
Functions of Several Variables
857
11
Partial Derivatives
868
9
Maxima and Minima
877
9
Maxima and Minima Using Lagrange Multipliers
886
10
Method of Least Squares
896
11
Double Integrals Over Rectangular Regions
907
18
Important Terms and Symbols
917
1
Review Exercise
918
3
Group Activity 1: City Planning
921
1
Group Activity 2: Numerical Integration of Multivariable Functions
922
3
Differential Equations
925
42
Basic Concepts
925
11
Separation of Variables
936
12
First-Order Linear Differential Equations
948
19
Important Terms and Symbols
959
1
Review Exercise
959
2
Group Activity 1: Torricelli's Law
961
2
Group Activity 2: Euler's Method
963
4
Probability and Calculus
967
48
Improper Integrals
967
8
Continuous Random Variables
975
13
Expected Value, Standard Deviation, and Median
988
9
Special Probability Distributions
997
18
Important Terms and Symbols
1008
1
Review Exercise
1009
3
Group Activity 1: Beta Distributions
1012
1
Group Activity 2: Chi-Square Distributions
1012
3
APPENDIX A Basic Algebra Review
1015
68
Self-Test on Basic Algebra
1015
2
A-1 Sets
1017
6
A-2 Algebra and Real Numbers
1023
7
A-3 Operations on Polynomials
1030
7
A-4 Factoring Polynomials
1037
6
A-5 Operations on Rational Expressions
1043
6
A-6 Integer Exponents and Scientific Notation
1049
6
A-7 Rational Exponents and Radicals
1055
7
A-8 Linear Equations and Inequalities in One Variable
1062
10
A-9 Quadratic Equations
1072
11
APPENDIX B Special Topics
1083
62
B-1 Sequences, Series, and Summation Notation
1083
7
B-2 Arithmetic and Geometric Sequences
1090
8
B-3 The Binomial Theorem
1098
3
B-4 Increments and Differentials
1101
8
B-5 L'Hopital's Rule
1109
11
B-6 Double Integrals over More General Regions
1120
9
B-7 Interpolating Polynomials and Divided Differences
1129
16
APPENDIX C Tables
1145
1
Table I Basic Geometric Formulas
1145
2
Table II Integration Formulas
1147
3
Table III Area under the Standard Normal Curve
1150
Answers
1
1
Index
1