Finite mathematics and applied calculus

1302 Pages·2011·72.99 MB·English

by  Stefan Waner, Steven R Costenoble

Finite Mathematics
and Applied Calculus
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Finite Mathematics
and Applied Calculus
Fifth Edition
Stefan Waner
Hofstra University
Steven R. Costenoble
Hofstra University
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Finite Mathematics and Applied © 2011, 2007Brooks/Cole, Cengage Learning
Calculus, Fifth Edition
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BRIEF CONTENTS
0 Precalculus Review 1
CHAPTER
1 Functions and Linear Models 39
CHAPTER
2 Systems of Linear Equations and Matrices 123
CHAPTER
3 Matrix Algebra and Applications 181
CHAPTER
4 Linear Programming 263
CHAPTER
5 The Mathematics of Finance 347
CHAPTER
6 Sets and Counting 395
CHAPTER
7 Probability 445
CHAPTER
8 Random Variables and Statistics 547
CHAPTER
9 Nonlinear Functions and Models 619
CHAPTER
10 Introduction to the Derivative 687
CHAPTER
11 Techniques of Differentiation with Applications 781
CHAPTER
12 Further Applications of the Derivative 865
CHAPTER
13 The Integral 947
CHAPTER
14 Further Integration Techniques and Applications
CHAPTER
of the Integral 1013
15 Functions of Several Variables 1079
CHAPTER
16 Trigonometric Models 1145
CHAPTER
v
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CONTENTS
0
Precalculus Review 1
CHAPTER
Introduction
0.1 Real Numbers 2
0.2 Exponents and Radicals 7
0.3 Multiplying and Factoring Algebraic Expressions 17
0.4 Rational Expressions 22
0.5 Solving Polynomial Equations 24
0.6 Solving Miscellaneous Equations 30
0.7 The Coordinate Plane 34
1
Functions and Linear Models 39
CHAPTER
Introduction
1.1 Functions from the Numerical, Algebraic, and Graphical Viewpoints 40
1.2 Functions and Models 56
1.3 Linear Functions and Models 75
1.4 Linear Regression 94
KEY CONCEPTS 104
REVIEW EXERCISES 104
CASE STUDY Modeling Spending on Internet Advertising 106
TECHNOLOGY GUIDES 110
2
Systems of Linear Equations and Matrices 123
CHAPTER
Introduction
2.1 Systems of Two Equations in Two Unknowns 124
2.2 Using Matrices to Solve Systems of Equations 137
2.3 Applications of Systems of Linear Equations 155
KEY CONCEPTS 168
REVIEW EXERCISES 168
CASE STUDY Hybrid Cars—Optimizing the Degree of Hybridization 171
TECHNOLOGY GUIDES 175
vii
viii Contents
3
Matrix Algebra and Applications 181
CHAPTER
Introduction
3.1 Matrix Addition and Scalar Multiplication 182
3.2 Matrix Multiplication 192
3.3 Matrix Inversion 206
3.4 Game Theory 217
3.5 Input-Output Models 233
KEY CONCEPTS 246
REVIEW EXERCISES 246
CASE STUDY Projecting Market Share 249
TECHNOLOGY GUIDES 254
4
Linear Programming 263
CHAPTER
Introduction
4.1 Graphing Linear Inequalities 264
4.2 Solving Linear Programming Problems Graphically 274
4.3 The Simplex Method: Solving Standard Maximization Problems 290
4.4 The Simplex Method: Solving General Linear Programming
Problems 307
4.5 The Simplex Method and Duality 320
KEY CONCEPTS 335
REVIEW EXERCISES 335
CASE STUDY The Diet Problem 339
TECHNOLOGY GUIDES 343
5
The Mathematics of Finance 347
CHAPTER
Introduction
5.1 Simple Interest 348
5.2 Compound Interest 356
5.3 Annuities, Loans, and Bonds 367
KEY CONCEPTS 380
REVIEW EXERCISES 380
CASE STUDY Adjustable Rate and Subprime Mortgages 382
TECHNOLOGY GUIDES 388
6
Sets and Counting 395
CHAPTER
Introduction
6.1 Sets and Set Operations 396
6.2 Cardinality 407
Contents ix
6.3 The Addition and Multiplication Principles 418
6.4 Permutations and Combinations 428
KEY CONCEPTS 441
REVIEW EXERCISES 441
CASE STUDY Designing a Puzzle 443
7
Probability 445
CHAPTER
Introduction
7.1 Sample Spaces and Events 446
7.2 Relative Frequency 460
7.3 Probability and Probability Models 468
7.4 Probability and Counting Techniques 487
7.5 Conditional Probability and Independence 495
7.6 Bayes’Theorem and Applications 512
7.7 Markov Systems 521
KEY CONCEPTS 536
REVIEW EXERCISES 536
CASE STUDY The Monty Hall Problem 539
TECHNOLOGY GUIDES 541
8
Random Variables and Statistics 547
CHAPTER
Introduction
8.1 Random Variables and Distributions 548
8.2 Bernoulli Trials and Binomial Random Variables 559
8.3 Measures of Central Tendency 567
8.4 Measures of Dispersion 580
8.5 Normal Distributions 594
KEY CONCEPTS 606
REVIEW EXERCISES 606
CASE STUDY Spotting Tax Fraud with Benford’s Law 608
TECHNOLOGY GUIDES 612
9
Nonlinear Functions and Models 619
CHAPTER
Introduction
9.1 Quadratic Functions and Models 620
9.2 Exponential Functions and Models 632
9.3 Logarithmic Functions and Models 647