# Course Content

The text book for this course is
`Industrial Mathematics. Modeling in Industry, Science, and Government.'
by Charles R. MacCluer, Prentice Hall, 2000.
These web pages will contain supplemental materials to the text book
and the lectures, mainly concerning the computational aspects of the
course.

### 1. statistical reasoning

L-1 The four most useful distributions
L-2 Taguchi quality control
L-3 Factor analysis and design of experiments

L-4 Proposals of projects, technical writing and presenting
### 2. The Monte Carlo method

L-5 mean time between failures and servicing requests
### 3. Data Acquisition and Manipulation

L-6 z-transforms
L-7 Simulations, Filters, and Stability Plots
L-8 Filters
L-9 Bode plots, feedback, and decibels
### 4. The Discrete Fourier Transform

L-10 cruise control and spectral analysis
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 Introduction to Linear Programming
L-16 LP continued and introduction to Regression.
### 6. Regression

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 answers
### 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 signals and ODEs, electronic circuits
L-27 Filters and Bode plots

L-28 Project II Presentations
L-29 Presentations of Project II (continued)

L-30 Control by Feedback
L-31 Root locus, Nyquist analysis and control
### 11. Partial Differential Equations

L-32 Air quality modeling by the advection equation with diffusion
L-33 Separation of variables applied to the heat equation
L-34 PDEs in Maple
L-35 Traffic Flow modeling
L-36 Periodic Steady State
### 12. Divided Differences

L-37 Numerical solving of ODEs and PDEs in Maple
### 13. Galerkin's method

L-38 Illustration of Galerkin's idea in Maple
L-39 Finite Elements
### 14. Splines

L-40 Illustration of Splines in Maple

L-13 Presentations of Project III
L-14 Presentations of Project III (continued)
L-15 Presentations of Project III (continued)