A Survey of Industrial Mathematics

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Overview

Students of mathematics, engineering, and science can learn how to apply classroom techniques to workplace problems with this concise single-volume text. It employs MATLAB and other strategies to resolve issues related to statistical reasoning, data acquisition, cost-benefit analysis, and other common workplace procedures.
Each chapter begins with a brief review of relevant mathematics, followed by an examination of the material's typical industrial applications. The author demonstrates the problem-solving power of interweaving analytic and computing methods and integrates MATLAB code into the narrative flow. Topics include the Monte Carlo method, the discrete Fourier transform, linear programming, regression, microeconomics, ordinary and partial differential equations, and frequency domain methods. A concluding chapter on technical writing explains how to present mathematical data in a variety of situations and offers helpful suggestions for assembling formal technical reports, progress reports, executive summaries, and other statements.

Product Details

• ISBN-13: 9780486477022
• Publisher: Dover Publications
• Publication date: 7/21/2010
• Series: Dover Books on Mathematics Series
• Pages: 384
• Sales rank: 999,889
• Product dimensions: 5.30 (w) x 8.40 (h) x 1.00 (d)

Preface ix

Acknowledgments xiv

1 Statistical Reasoning 1

1.1 Random Variables 1

1.2 Uniform Distributions 5

1.3 Gaussian Distributions 6

1.4 The Binomial Distribution 7

1.5 The Poisson Distribution 10

1.6 Taguchi Quality Control 12

Exercises 16

2 The Monte Carlo Method 21

2.1 Computing Integrals 21

2.2 Mean Time Between Failures 23

2.3 Servicing Requests 24

2.4 The Newsboy Problem (Reprise) 27

Exercises 28

3 Data Acquisition and Manipulation 31

3.1 The z-Transform 31

3.2 Linear Recursions 34

3.3 Filters 36

3.4 Stability 39

3.5 Polar and Bode Plots 40

3.6 Aliasing 46

3.7 Closing the Loop 47

3.8 Why Decibels? 51

Exercises 53

4 The Discrete Fourier Transform 59

4.1 Real Time Processing 59

4.2 Properties of the DFT 61

4.3 Filter Design 63

4.4 The Fast Fourier Transform 66

4.5 Image Processing 70

Exercises 74

5 Linear Programming 77

5.1 Optimization 77

5.2 The Diet Problem 80

5.3 The Simplex Algorithm 81

6 Regression 89

6.1 Best Fit to Discrete Data 89

6.2 Norms on Rn 93

6.3 Hilbert Space 94

6.4 Gram's Theorem on Regression 97

Exercises 101

7 Cost-Benefit Analysis 105

7.1 Present Value 105

7.2 Life-Cycle Savings 106

Exercises 108

8 Microeconomics 111

8.1 Supply and Demand 111

8.2 Revenue, Cost, and Profit 113

8.3 Elasticity of Demand 115

8.4 Duopolistic Competition 116

8.5 Theory of Production 118

8.6 Leontief Input/Output 119

Exercises 121

9 Ordinary Differential Equations 123

9.1 Separation of Variables 123

9.2 Mechanics 127

9.3 Linear ODEs with Constant Coefficients 130

9.4 Systems 135

Exercises 142

10 Frequency-Domain Methods 149

10.1 The Frequency Domain 149

10.2 Generalized Signals 153

10.4 Surge Impedance 159

10.5 Stability 161

10.6 Filters 164

10.7 Feedback and Root Locus 169

10.8 Nyquist Analysis 173

10.9 Control 179

Exercises 184

11 Partial Differential Equations 191

11.1 Lumped versus Distributed 191

11.2 The Big Six PDEs 192

11.3 Separation of Variables 194

11.4 Unbounded Spatial Domains 213

11.6 Other Distributed Models 217

Exercises 223

12 Divided Differences 231

12.1 Euler's Method 231

12.2 Systems 234

12.3 PDEs 235

12.4 Runge-Kutta Method 240

Exercises 240

13 Galerkin's Method 243

13.1 Galerkin's Requirement 243

13.2 Eigenvalue Problems 247

13.4 Transient Problems 250

13.5 Finite Elements 252

13.6 Why So Effective? 259

Exercises 262

14 Splines 265

14.1 Why Cubics? 265

14.2 m-Splines 267

14.3 Cubic Splines 269

Exercises 274

15 Report Writing 277

15.1 The formal Technical Report 277

15.2 The Memo 282

15.3 The Progress Report 284

15.4 The Executive Summary 284

15.5 The Problem Statement 285

15.6 Projector Presentations 286

15.7 Approaching a Writing Task 287

15.8 Style 288

15.9 Writer's checklist 291

Appendix B: Selected Solutions 303

References 355

Index 361

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