Finite Mathematics and Applied Calculus, 4th Edition (with Personal Tutor, Premium Web Site Printed Access Card)

1252 Pages·2006·38.5 MB·English

by  Stefan Waner

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Finite Mathematics
and Applied Calculus
Fourth Edition
STEFAN WANER Hofstra University
STEVEN R. COSTENOBLE Hofstra University
Australia • Brazil • Canada • Mexico • Singapore
Spain • United Kingdom • United States
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Finite Mathematics and Applied Calculus,Fourth Edition
Stefan Waner and Steven R. Costenoble
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Finite Mathematics
and Applied Calculus
Fourth Edition
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Brief Contents
Chapter 0 Algebra Review 1
Chapter 1 Functions and Linear Models 33
Chapter 2 Systems of Linear Equations and Matrices 113
Chapter 3 Matrix Algebra and Applications 173
Chapter 4 Linear Programming 257
Chapter 5 The Mathematics of Finance 341
Chapter 6 Sets and Counting 393
Chapter 7 Probability 443
Chapter 8 Random Variables and Statistics 543
Chapter 9 Nonlinear Models 615
Chapter 10 Introduction to the Derivative 685
Chapter 11 Techniques of Differentiation 797
Chapter 12 Applications of the Derivative 851
Chapter 13 The Integral 919
Chapter 14 Further Integration Techniques and
Applications of the Integral 981
Chapter 15 Functions of Several Variables 1041
Chapter 16 Trigonometric Models 1111
Chapter S Calculus Applied to Probability and Statistics (ONLINE)
Appendix A Logic A1
Appendix B Table: Area Under a Normal Curve A17
Answers to Selected Exercises A18
Index I-1
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Contents
Chapter 0 Algebra Review 1
Introduction 2
0.1 Real Numbers 2
0.2 Exponents and Radicals 8
0.3 Multiplying and Factoring Algebraic Expressions 17
0.4 Rational Expressions 21
0.5 Solving Polynomial Equations 23
0.6 Solving Miscellaneous Equations 29
Chapter 1 Functions and Linear Models 33
Introduction 34
1.1 Functions from the Numerical and Algebraic Viewpoints 34
1.2 Functions from the Graphical Viewpoint 44
1.3 Linear Functions 55
1.4 Linear Models 66
1.5 Linear Regression 82
Key Concepts 93
Review Exercises 93
Case Study Modeling Spending on Internet Advertising 95
Technology Guides 99
Optional Online Topic New Functions from Old: Scaled and Shifted Functions
Chapter 2 Systems of Linear Equations and Matrices 113
Introduction 114
2.1 Systems of Two Equations in Two Unknowns 114
2.2 Using Matrices to Solve Systems of Equations 127
2.3 Applications of Systems of Linear Equations 145
Key Concepts 159
Review Exercises 159
Case Study The Impact of Regulating Sulfur Emissions 162
Technology Guides 165
Chapter 3 Matrix Algebra and Applications 173
Introduction 174
3.1 Matrix Addition and Scalar Multiplication 174
3.2 Matrix Multiplication 184
3.3 Matrix Inversion 198
3.4 Game Theory 209
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vi Contents
3.5 Input-Output Models 226
Key Concepts 238
Review Exercises 238
Case Study The Japanese Economy 241
Technology Guides 244
Chapter 4 Linear Programming 257
Introduction 258
4.1 Graphing Linear Inequalities 258
4.2 Solving Linear Programming Problems Graphically 269
4.3 The Simplex Method: Solving Standard Maximization Problems 285
4.4 The Simplex Method: Solving General Linear Programming Problems 302
4.5 The Simplex Method and Duality (OPTIONAL) 315
Key Concepts 329
Review Exercises 329
Case Study Airline Scheduling 332
Technology Guides 336
Chapter 5 The Mathematics of Finance 341
Introduction 342
5.1 Simple Interest 342
5.2 Compound Interest 350
5.3 Annuities, Loans, and Bonds 360
Key Concepts 374
Review Exercises 374
Case Study Saving for College 376
Technology Guides 380
Chapter 6 Sets and Counting 393
Introduction 394
6.1 Sets and Set Operations 394
6.2 Cardinality 405
6.3 The Addition and Multiplication Principles 416
6.4 Permutations and Combinations 426
Key Concepts 439
Review Exercises 439
Case Study Designing a Puzzle 441
Chapter 7 Probability 443
Introduction 444
7.1 Sample Spaces and Events 444
7.2 Estimated and Theoretical Probability 457
7.3 Properties of Probability Distributions 473
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7.4 Probability and Counting Techniques (OPTIONAL) 483
7.5 Conditional Probability and Independence 491
7.6 Bayes’Theorem and Applications 507
7.7 Markov Systems 517
Key Concepts 531
Review Exercises 531
Case Study The Monty Hall Problem 534
Technology Guides 536
Chapter 8 Random Variables and Statistics 543
Introduction 544
8.1 Random Variables and Distributions 544
8.2 Bernoulli Trials and Binomial Random Variables 554
8.3 Measures of Central Tendency 562
8.4 Measures of Dispersion 574
8.5 Normal Distributions 589
Key Concepts 601
Review Exercises 601
Case Study Spotting Tax Fraud with Benford’s Law 603
Technology Guides 607
Optional Online Topics Sampling Distributions and the Central Limit Theorem
Confidence Intervals
Hypothesis Testing
Chapter 9 Nonlinear Models 615
Introduction 616
9.1 Quadratic Functions and Models 616
9.2 Exponential Functions and Models 628
9.3 Logarithmic Functions and Models 645
9.4 Logistic Functions and Models 658
Key Concepts 667
Review Exercises 667
Case Study Checking up on Malthus 670
Technology Guides 674
Optional Online Topics Inverse Functions
Using and Deriving Algebraic Properties of Logarithms
Chapter 10 Introduction to the Derivative 685
Introduction 686
10.1 Limits: Numerical and Graphical Approaches (OPTIONAL) 686
10.2 Limits and Continuity (OPTIONAL) 698
10.3 Limits and Continuity: Algebraic Approach (OPTIONAL) 703
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10.4 Average Rate of Change 712
10.5 Derivatives: Numerical and Graphical Viewpoints 727
10.6 The Derivative: Algebraic Viewpoint 749
10.7 Derivatives of Powers, Sums, and Constant Multiples 758
10.8 A First Application: Marginal Analysis 772
Key Concepts 783
Review Exercises 783
Case Study Reducing Sulfur Emissions 787
Technology Guides 790
Optional Online Topics Sketching the Graph of the Derivative
Proof of the Power Rule
Continuity and Differentiability
Chapter 11 Techniques of Differentiation 797
Introduction 798
11.1 The Product and Quotient Rules 798
11.2 The Chain Rule 810
11.3 Derivatives of Logarithmic and Exponential Functions 822
11.4 Implicit Differentiation (OPTIONAL) 839
Key Concepts 841
Review Exercises 841
Case Study Projecting Market Growth 843
Optional Online Topic Linear Approximation and Error Estimation
Chapter 12 Applications of the Derivative 851
Introduction 852
12.1 Maxima and Minima 852
12.2 Applications of Maxima and Minima 865
12.3 The Second Derivative and Analyzing Graphs 878
12.4 Related Rates 893
12.5 Elasticity 902
Key Concepts 911
Review Exercises 911
Case Study Production Lot Size Management 913
Technology Guides 917
Chapter 13 The Integral 919
Introduction 920
13.1 The Indefinite Integral 920
13.2 Substitution 932
13.3 The Definite Integral: Numerical and Graphical Approaches 941
13.4 The Definite Integral: Algebraic Approach and the Fundamental
Theorem of Calculus 959
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Contents ix
Key Concepts 969
Review Exercises 969
Case Study Wage Inflation 971
Technology Guides 976
Optional Online Topic Numerical Integration
Chapter 14 Further Integration Techniques and Applications
of the Integral 981
Introduction 982
14.1 Integration by Parts 982
14.2 Area Between Two Curves and Applications 989
14.3 Averages and Moving Averages 996
14.4 Applications to Business and Economics: Consumers’and Producers’
Surplus and Continuous Income Streams (OPTIONAL) 1004
14.5 Improper Integrals and Applications 1014
14.6 Differential Equations and Applications 1023
Key Concepts 1031
Review Exercises 1031
Case Study Estimating Tax Revenues 1033
Technology Guides 1038
Chapter 15 Functions of Several Variables 1041
Introduction 1042
15.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints 1042
15.2 Three-Dimensional Space and the Graph of a Function of Two Variables 1054
15.3 Partial Derivatives 1064
15.4 Maxima and Minima 1073
15.5 Constrained Maxima and Minima and Applications 1082
15.6 Double Integrals and Applications 1089
Key Concepts 1098
Review Exercises 1098
Case Study Modeling Household Income 1100
Technology Guides 1108
Chapter 16 Trigonometric Models 1111
Introduction 1112
16.1 Trigonometric Functions, Models, and Regression 1112
16.2 Derivatives of Trigonometric Functions and Applications 1125
16.3 Integrals of Trigonometric Functions and Applications 1132
Key Concepts 1140
Review Exercises 1140
Case Study Predicting Cocoa Inventories 1141
Technology Guides 1144