Industrial Mathematics: Modeling in Industry, Science and Government, 1/e
Charles R. MacCluer, Michigan State University
Published August, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 308 pp.
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For senior-level or masters courses in Industrial Mathematics
This concise, single-source survey of all the mathematics
most useful in industry, provides graduating seniors or MS students
with a last chance to prepare for the marketplace. Typically,
such students are well grounded in the fundamentals of mathematics
but not in its practice. They usually have little experience
in modeling or in the particular extensions of mathematics useful
in industrial problemse.g., they may know power series but not
the z-transform, orthogonal matrices but not factor analysis, Laplace
transforms but not Bode Plots. Likewise, they usually have no experience
with problems incorporating the unit $. Mathematicians in industry
must be able to see their work from an economic viewpoint. They must
be able to communicate with engineers using their common dialect,
the dialect of this book.
Sparse, brief writing style.
Relevant mathematics, then real-world industrial extensionsEach
chapter begins with a brief review of some relevant mathematics, then
introduces the industrial extension of this same material via typical
- Speaks to seasoned mathematics, engineering, and science
students in language with which they are comfortable.
A modern approach to problem solvingDemonstrates
the power of interweaving analytic with computing
methods during problem solving.
- Ensures that students have a firm understanding of
the mathematics before tackling applications and familiarizes
students with the full range of applications they are likely to encounter
in the workplace.
MATLAB incorporated into exercisesMany exercises
require students to experiment with or to modify the given MATLAB
routines, all of which are available at the author's anonymous ftp
site. Other exercises ask students to generate code themselves.
- A modern mathematics worker in industry cannot be
fully effective without both analytic and computing skills.
Open-ended exercises marked as ProjectsRequire
students to delimit the investigation, collect data, experiment, or
consult industrial experts; organize the data; then deliver the data
in a formal technical report.
- MATLAB has become the industry-wide, standard computing
and simulation tool. Familiarity with MATLAB will be invaluable on
the job and at interview time.
A chapter on Technical WritingCovers formal
technical reports, memos, progress reports, executive summaries, problem
statements, and overhead projector presentations.
- The student is exposed to team project development,
universal in industry.
- Communication skills are essential to success. Workers
in industry are judged not on their work but on how they present their
(NOTE: Each chapter concludes with Exercises.)
1. Statistical Reasoning.
Random Variables. Uniform Distributions. Gaussian Distributions.
The Binomial Distribution. The Poisson Distribution. Taguchi Quality
2. Monte Carlo Methods.
Computing Integrals. Mean Time between Failure. Servicing
Requests. The Newsboy Problem (reprise).
3. Data Acquisition and Manipulation.
The z-transform. Linear Recursions. Filters. Stability.
Polar and Bode Plots. Aliasing. Closing the Loop. Why Decibels?
4. The Discrete Fourier Transform.
Real Time Processing. Properties of the DFT. Filter Design.
The Fast Fourier Transform. Image Processing.
5. Linear Programming.
Optimization. The Diet Problem. The Simplex Algorithm.
Best Fit to Discrete Data. Norms on R^n. Hilbert Space.
Gram's Theorem on Regression.
7. Cost Benefit Analysis.
Present Value. Life-Cycle Savings.
Supply and Demand. Revenue, Cost, and Profit. Elasticity
of Demand. Duopolistic Competition. Theory of Production. Leontiev
9. Ordinary Differential Equations.
Separation of Variables. Mechanics. Linear ODEs with Constant
10. Frequency-Domain Methods.
The Frequency Domain. Generalized Signals. Plants in Cascade.
Surge Impedance. Stability. Filters. Feedback and Root Locus. Nyquist
11. Partial Differential Equations.
Lumped versus Distributed. The Big Six PDEs. Separation
of Variables. Unbounded Spatial Domains. Periodic Steady State. Other
12. Divided Differences.
Euler's Method. Systems. PDEs. Runge-Kutta Method.
13. Galerkin's Method.
Galerkin's Requirement. Eigenvalue Problems. Steady Problems.
Transient Problems. Finite Elements. Why So Effective?
Why Cubics? m-Splines. Cubic Splines.
15. Report Writing.
The Formal Technical Report. The Memo. The Progress Report.
The Executive Summary. The Problem Statement. Overhead Projector Presentations.
Approaching a Writing Task. Style. Writer's Checklist.