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Tables of Contents for Mathematics With Applications
Chapter/Section Title
Page #
Page Count
Preface
ix
6
To the Student
xv
 
CHAPTER 1 Algebra and Graphs
1
71
1.1 The Real Numbers
1
10
1.2 First-Degree Equations
11
10
1.3 Polynomials
21
5
1.4 Factoring
26
4
1.5 Graphs
30
13
1.6 Slope and the Equations of a Line
43
11
1.7 Applications of Linear Equations
54
12
Chapter 1 Summary
66
1
Chapter 1 Review Exercises
67
3
Case 1 Consumers Often Defy Common Sense
70
2
CHAPTER 2 Equations and Inequalities
72
35
2.1 Graphical and Numerical Solutions of Equations
72
7
2.2 Quadratic Equations
79
9
2.3 Linear Inequalities
88
7
2.4 Polynomial and Rational Inequalities
95
8
Chapter 2 Summary
103
1
Chapter 2 Review Exercises
104
1
Case 2 Depreciation
105
2
CHAPTER 3 Functions and Graphs
107
45
3.1 Functions
107
8
3.2 Graphs of Functions
115
12
3.3 Applications of Linear Functions
127
9
3.4 Quadratic Functions
136
5
3.5 Applications of Quadratic Functions
141
8
Chapter 3 Summary
149
1
Chapter 3 Review Exercises
149
2
Case 3 Marginal Cost-Booz, Allen and Hamilton
151
1
CHAPTER 4 Polynomial and Rational Functions
152
29
4.1 Polynomial Functions
152
7
4.2 Applications of Polynomial Functions
159
5
4.3 Rational Expressions
164
5
4.4 Rational Functions
169
9
Chapter 4 Summary
178
1
Chapter 4 Review Exercises
178
2
Case 4 Error-Correcting Codes
180
1
CHAPTER 5 Exponential and Logarithmic Functions
181
44
5.1 Exponents and Radicals
181
9
5.2 Exponential Functions
190
8
5.3 Applications of Exponential Functions
198
6
5.4 Logarithmic Functions
204
10
5.5 Applications of Logarithmic Functions
214
6
Chapter 5 Summary
220
1
Chapter 5 Review Exercises
221
2
Case 5 Characteristics of the Monkeyface Prickleback
223
2
CHAPTER 6 Mathematics of Finance
225
40
6.1 Simple Interest and Discount
225
6
6.2 Compound Interest
231
9
6.3 Annuities
240
10
6.4 Present Value of an Annuity; Amortization
250
6
6.5 Applying Financial Formulas
256
3
Chapter 6 Summary
259
1
Chapter 6 Review Exercises
260
3
Case 6 Time, Money, and Polynomials
263
2
CHAPTER 7 Systems of Linear Equations and Matrices
265
59
7.1 Systems of Linear Equations
265
14
7.2 The Gauss-Jordan Method
279
8
7.3 Basic Matrix Operations
287
8
7.4 Matrix Products and Inverses
295
12
7.5 Applications of Matrices
307
9
Chapter 7 Summary
316
2
Chapter 7 Review Exercises
318
3
Case 7 Leontief's Model of the American Economy
321
3
CHAPTER 8 Linear Programming
324
67
8.1 Graphing Linear Inequalities in Two Variables
324
8
8.2 Linear Programming: The Graphical Method
332
8
8.3 Applications of Linear Programming
340
7
8.4 The Simplex Method: Maximization
347
13
8.5 Maximization Applications
360
5
8.6 The Simplex Method: Duality and Minimization
365
9
8.7 The Simplex Method: Nonstandard Problems
374
11
Chapter 8 Summary
385
1
Chapter 8 Review Exercises
386
4
Case 8 A Minimum Cost Balanced Organic Fertilizer Mix
390
1
CHAPTER 9 Sets and Probability
391
60
9.1 Sets
391
9
9.2 Applications of Venn Diagrams
400
9
9.3 Probability
409
7
9.4 Basic Concepts of Probability
416
11
9.5 Conditional Probability; Independent Events
427
12
9.6 Bayes' Formula
439
7
Chapter 9 Summary
446
1
Chapter 9 Review Exercises
447
3
Case 9 Medical Diagnosis
450
1
CHAPTER 10 Further Topics in Probability
451
55
10.1 Permutations and Combinations
451
12
10.2 Applications of Counting
463
6
10.3 Binomial Probability
469
5
10.4 Markov Chains
474
10
10.5 Probability Distributions; Expected Value
484
12
10.6 Decision Making
496
4
Chapter 10 Summary
500
1
Chapter 10 Review Exercises
501
3
Case 10 Optimal Inventory for a Service Truck
504
2
CHAPTER 11 Introduction to Statistics
506
41
11.1 Frequency Distributions; Measures of Central Tendency
506
10
11.2 Measures of Variation
516
9
11.3 Normal Distributions
525
10
11.4 Binomial Distributions
535
7
Chapter 11 Summary
542
1
Chapter 11 Review Exercises
543
2
Case 11 Statistical Process Control
545
2
CHAPTER 12 Differential Calculus
547
90
12.1 Limits
547
11
12.2 Rates of Change
558
10
12.3 Tangent Lines and Derivatives
568
17
12.4 Techniques for Finding Derivatives
585
12
12.5 Derivatives of Products and Quotients
597
7
12.6 The Chain Rule
604
10
12.7 Derivatives of Exponential and Logarithmic Functions
614
7
12.8 Continuity and Differentiability
621
9
Chapter 12 Summary
630
2
Chapter 12 Review Exercises
632
3
Case 12 Price Elasticity of Demand
635
2
CHAPTER 13 Applications of the Derivative
637
44
13.1 Derivatives and Graphs
637
14
13.2 The Second Derivative
651
12
13.3 Optimization Applications
663
14
Chapter 13 Summary
677
1
Chapter 13 Review Exercises
677
2
Case 13 A Total Cost Model for a Training Program
679
2
CHAPTER 14 Integral Calculus
681
61
14.1 Antiderivatives
681
9
14.2 Integration by Substitution
690
7
14.3 Area and the Definite Integral
697
11
14.4 The Fundamental Theorem of Calculus
708
9
14.5 Applications of Integrals
717
10
14.6 Differential Equations
727
9
Chapter 14 Summary
736
1
Chapter 14 Review Exercises
737
3
Case 14 Estimating Depletion Dates for Minerals
740
2
CHAPTER 15 Multivariate Calculus
742
29
15.1 Functions of Several Variables
742
9
15.2 Partial Derivatives
751
9
15.3 Extrema of Functions of Several Variables
760
7
Chapter 15 Summary
767
2
Chapter 15 Review Exercises
769
2
Appendix A Program Appendix
771
20
Appendix B Tables
791
 
Answers to Selected Exercises
A-1
 
Index of Applications
I-1
 
Index
I-7