Industrial Mathematics

`modeling in industry, science, and government`
C. R. MacCluer,  Prentice Hall,  2000
This book is for senior, or masters student of mathematics, engineering,or science about to enter the workforce. The book surveys the mathematicsof most use in industry. The graduate may be well- grounded in the fundamentalsof mathematics but not in its practice. Although changing of late throughthe efforts of COMAP, SIAM, and NSA, the graduating student has littleexperience in modeling or in the particular extensions of mathematics usefulin industrial problems. They may know power series but not the z-transform,orthogonal matrices but not factor analysis, Laplace transforms but notBode Plots. Most certainly they will have no experience with problems incorporatingthe unit \$. Mathematicians in industry must be able to see their work froman economic viewpoint. They must also be able to communicate with engineersusing their common dialect, the dialect of this book.

Scripts  for the MATLAB routines used in the bookare found at the MathWorks ftp site
ftp://ftp.mathworks.com/pub/books/maccluer

Ordering information is to be found at PrenticeHall

Sample chapters are available in Latex source code fromthe author maccluer@math.msu.edu.

This text is used in the Survey of Industrial Mathematics843 of ourIndustrial MathematicsMS program.

Preface

To the instructor
Chapter interdependence

1. Statistical reasoning

1.1 Random variables
1.2 Uniform distributions
1.3 Gaussian distributions
1.4 The binomial distribution
1.5 The Poisson distribution
1.6 Taguchi quality control

2. Monte Carlo methods

2.1 Computing integrals
2.2 Mean time between failure (MTBF)
2.3 Servicing requests
2.4 The newsboy problem (reprise)

3. Data acquisition and manipulation

3.1 The z-transform
3.2 Linear recursions
3.3 Filters
3.4 Stability
3.5 Polar and Bode plots
3.6 Aliasing
3.7 Closing the loop
3.8 Why decibels?

4. The discrete Fourier transform (DFT)

4.1 Realtime processing
4.2 Properties of the DFT
4.3 Filter design
4.4 The fast Fourier transform (FFT)
4.5 Image processing

5. Linear programming

5.1 Optimization
5.2 The Diet Problem
5.3 The Simplex Algorithm

6. Regression

6.1 Best fit to discrete data
6.2 Norms on R^{n}
6.3 Hilbert space
6.4 Gram's theorem on regression

7. Cost benefit analysis

7.1 Present value
7.2 Life cycle costing

8. Microeconomics

8.1 Supply and demand
8.2 Revenue, cost, and profit
8.3 Elasticity of demand
8.4 Duopolistic competition
8.5 Theory of production
8.6 Leontiev input/output

9. Ordinary differential equations

9.1 Separation of variables
9.2 Mechanics
9.3 Linear ODEs with constant coefficients
9.4 Systems

10. Frequency domain methods

10.1 The frequency domain
10.2 Generalized signals
10.4 Surge impedance
10.5 Stability
10.6 Filters
10.7 Feedback and root-locus
10.8 Nyquist analysis
10.9 Control

11. Partial differential equations

11.1 Lumped versus distributed
11.2 The big six PDEs
11.3 Separation of variables
11.4 Unbounded spatial domains
11.6 Other distributed models

12. Divided differences

12.1 Euler's method
12.2 Systems
12.3 PDEs
12.4 Runge-Kutta

13. Galerkin's method

13.1 Galerkin's requirement
13.2 Eigenvalue problems
13.4 Transient problems
13.5 Finite elements
13.6 Why so effective?

14. Splines

14.1 Why cubics?
14.2 m-Splines
14.3 Cubic splines

15. Report writing

15.1 The formal technical report
15.2 The memo
15.3 Progress reports
15.4 Executive summaries
15.5 Problem statements
15.8 Style
15.9 Writers checklist

Index

Contact: maccluer@math.msu.edu

Last Revised 12/20/96