# Course Content

The text book for this course is
`Industrial Mathematics. Modeling in Industry, Science, and Government.'
by Charles R. MacCluer, Prentice Hall, 2000.
Industrial mathematics is mathematics subject to the constraints
of time and money. Unlike pure mathematicians, we do not
have the luxury to think for centuries about resolving a conjecture,
but must come up with a solution which makes our business more
profitable in a very limited time frame.
Almost without exception, the solution will involve computations.
Unfortunately, we do not have the time nor the means to develop
tailored programs, so we better take advantage of available
software tools.
Thirdly, the reward for our work is directly linked to our
ability to present our solution for a non-mathematical and very
busy readership. While these tasks seem daunting, do not worry,
teamwork is essential, we collaborate.

These web pages will contain supplemental materials to the text book
and the lectures, mainly concerning the computational aspects of the
course.

Below are some supplemental materials to the lectures.

## 1. Statistical Reasoning

L-1 The four most useful distributions
L-2 Maple solution to a staffing problem
## 2. The Monte Carlo Method

L-3 Maple solution to the mean time between failures problem
L-4 Presentations of projects and technical writing
L-5 MTBF and servicing requests
## 3. Data Aquisition and Manipulation

L-6 Z-transforms and linear recursions
L-7 Filters, Stability, and plots
L-8 Filters
L-9 Control Systems Design
## 4. The Discrete Fourier Transform

L-10 The FFT and its application to filters
L-11 The DFT: definition, properties and filter design
L-12 The FFT and image processing

L-13 Presentations of Project I
L-14 Presentations of Project I (continued)
## 5. Linear Programming

L-15 Linear Programming
## 6. Regression

L-16 Linear programming and polynomial fitting in MATLAB
L-17 Regression
## 7. Cost-Benefit Analysis

L-18 Fourier Series and Cost-Benefit Analysis
## 8. Microeconomics

L-19 Microeconomics
L-20 Macroeconomics

L-21 Midterm Exam on Chapters 1 to 8
with solutions
## 9. Ordinary Differential Equations

L-22 ODEs in mechanics
L-23 Linear ODEs with constant coefficients
L-24 Linear Systems
## 10. Frequency-Domain Methods

L-25 Frequency domains, signals, and plants
L-26 Plants, signals, and surge impedance
L-27 Filters and Bode plots
L-28 Project II Presentations, Feedback and Root Locus
L-29 Presentations of Project II (continued)
L-30 Project II presentation (continued) and Nyquist Analysis
L-31 Nyquist plots and Control
## 11. Partial Differential Equations

L-32 Air Quality Modeling
L-33 Separation of Variables
L-34 PDEs in Maple
L-35 Traffic Flow Modeling
L-36 Periodic Steady State
## 12. Divided Differences

L-37 Numerically Solving ODEs and PDEs with Maple
## 13. Galerkin's method

L-38 Galerkin's method in Maple
L-39 Finite elements
## 14. Splines

L-40 Splines
L-41 Splines continued and review
L-42 Presentations of Project III
L-43 Presentations of Project III (continued)