Mathematical Modeling (Math512 sec. 010 & 080) Fall 2001
MW 1430-1520 Mem 108 & F 1430-1520 Mem 109
©2001 L. F. Rossi All rights reserved.

Prof. L. F. Rossi
Office: Ewg 524
Telephone: x1880
Email: rossi@math.udel.edu
WWW: http://www.math.udel.edu/$\sim$rossi

Your objective: You will learn to use calculus, linear algebra, differential equations and everything else you have learned to solve everyday problems. Ultimately, you must develop an intuition and resourcefulness about solving problems.

Your resources: All of the following will help you achieve your objectives:

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Time: Attendance in this course is mandatory.

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Office hours: Mon 1300-1400, Wed 1300-1400, Thurs 1000-1100 or by appointment. Office hours are one of the most valuable and least used resources at the University, and I hope you will take advantage of them. I want to help you learn this material, so do not be shy about seeing me outside of class. Your exams will only be distributed during office hours. If you need to see me at a time other than an office hour, feel free to ``drop in'' or make an appointment.

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Your classmates: Math is not a competitive sport. There are many obvious reasons to work together. Even if you end up helping others most of the time, teaching is one of the best ways to gain a deeper understanding of a subject. In fact, half of your grade in this course is a team effort.

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Textbooks & library research: There is no required textbook for this class, but you will want to keep a few books handy. First, if your fundamentals are a bit rusty, you should dust off your calculus textbook. Next, a standard text on ordinary differential equations and linear algebra will definitely be useful. I will play general modeling texts on reserve in the library. Also, I expect students to visit the library frequently to fill in gaps in their knowledge.

Themes:

This course will have several common themes that run through every subject.

• Modeling: What is a model? What is not? Is the model under consideration sufficient to answer the question at hand? How can we assess the strengths and weaknesses of the model?

• What is the structure of an effective solution to a problem? Who is the audience? What is your objective and what role does the audience play?

Tentative topics:

• Scaling, dimensional analysis and dimensionless constants: Converting units, scale experiments, dynamic similarity...

• Working with data I. Interpolation, least squares, parameter estimation, splines.

• Conservations laws: Partial differential equations, flux, diffusion, wave propagation, Helmholtz equation, traffic, pipe flows...

• Working with data II. Assessing the quality of a model. Norms and metrics.

• Coding theory. The football pool problem. The colored hat problem. Hamming codes.

• Signal processing, frequency domain, scale domain, sampling, bias, etc.

Regular problem sets:

At regular intervals of approximately one week, you will be required to complete problem sets.

Projects:

You will be required to complete three projects. Projects are open-ended questions taken from previous Mathematical Contest in Modeling problems and other sources. There is no ``answer in the back of the book.'' You will be permitted to work in groups of up to three people on these problems, and there will be individual oral exams based on your projects.

The first two projects will have the form of a full written report. This report should have an complete introduction with all relevant background information, a statement of assumptions, an analysis and solution the problem, an assessment of the quality of your solution and a conclusion. The last project presentation will be oral followed by an on-site comparison of competing solutions. I expect all projects to be complete and concise.

Final exam:

There will be a brief final exam at the end of the semester on traditional topics surveyed in the course.

Grading policy:

Your grade is determined solely by your participation, problem sets and final project.

Homework	20%
Class participation	10%
Projects	30%
Oral exam	30%
Final exam	10%

Final letter grades will be assigned strictly based on the following percentages of your total point score:
100 $\leftarrow$ A $\rightarrow$ 93 $\leftarrow$ A- $\rightarrow$ 90 $\leftarrow$ B+ $\rightarrow$ 87 $\leftarrow$ B $\rightarrow$ 83 $\leftarrow$ B- $\rightarrow$ 80 $\leftarrow$ C+ $\rightarrow$ 77 $\leftarrow$ C
C $\rightarrow$ 73 $\leftarrow$ C- $\rightarrow$ 70 $\leftarrow$ D+ $\rightarrow$ 67 $\leftarrow$ D $\rightarrow$ 63 $\leftarrow$ D- $\rightarrow$ 60 $\leftarrow$ F $\rightarrow$ 0



I reserve the right to adjust this scale to improve grades if the course material proves to be unreasonably demanding.