[Book Cover]

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.
Cloth
ISBN 0-13-949199-6


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Summary

For senior-level or masters courses in Industrial Mathematics or Modeling. 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 problems—e.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.

Features


Sparse, brief writing style.

  • Speaks to seasoned mathematics, engineering, and science students in language with which they are comfortable.
Relevant mathematics, then real-world industrial extensions—Each chapter begins with a brief review of some relevant mathematics, then introduces the industrial extension of this same material via typical real-world applications.
  • 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.
A modern approach to problem solving—Demonstrates the power of interweaving analytic with computing methods during problem solving.
  • A modern mathematics worker in industry cannot be fully effective without both analytic and computing skills.
MATLAB incorporated into exercises—Many 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.
  • MATLAB has become the industry-wide, standard computing and simulation tool. Familiarity with MATLAB will be invaluable on the job and at interview time.
Open-ended exercises marked as “Projects”—Require students to delimit the investigation, collect data, experiment, or consult industrial experts; organize the data; then deliver the data in a formal technical report.
  • The student is exposed to team project development, universal in industry.
A chapter on Technical Writing—Covers formal technical reports, memos, progress reports, executive summaries, problem statements, and overhead projector presentations.
  • Communication skills are essential to success. Workers in industry are judged not on their work but on how they present their work.


Table of Contents
(NOTE: Each chapter concludes with Exercises.)
    1. Statistical Reasoning.

      Random Variables. Uniform Distributions. Gaussian Distributions. The Binomial Distribution. The Poisson Distribution. Taguchi Quality Control.

    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.

    6. Regression.

      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.

    8. Microeconomics.

      Supply and Demand. Revenue, Cost, and Profit. Elasticity of Demand. Duopolistic Competition. Theory of Production. Leontiev Input/Output.

    9. Ordinary Differential Equations.

      Separation of Variables. Mechanics. Linear ODEs with Constant Coefficients. Systems.

    10. Frequency-Domain Methods.

      The Frequency Domain. Generalized Signals. Plants in Cascade. Surge Impedance. Stability. Filters. Feedback and Root Locus. Nyquist Analysis. Control.

    11. Partial Differential Equations.

      Lumped versus Distributed. The Big Six PDEs. Separation of Variables. Unbounded Spatial Domains. Periodic Steady State. Other Distributed Models.

    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?

    14. Splines.

      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.

    References.
    Index.


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