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| Course: | MATH 481: Mathematical Modeling |
| Time/Place: | MW 4:00pm–5:15pm, SOND 105 |
| Instructor: | Dr. Rouben Rostamian |
| Office: | MP 402 |
| Phone: | 410–455–2458 |
| Email: | rostamian@umbc.edu |
| Office hours: | MW 3:00–4:00, and by appointment |
| Course web page: | http://www.math.umbc.edu/~rouben/2008-01-math481/ |
Mathematical Modeling with Case Studies:
A Differential Equation Approach Using Maple
by
Belinda Barnes
and
Glenn Fulford.
We will cover a wide selection of topics from this book, as time permits.
Mathematical modeling refers to the process of applying mathematical tools and reasoning to understand the world around us. In this course we will get a glimpse of such process in the context a large number of case studies in Barnes and Fulford's book. Here is a small sampling of cases in that book. We will analyze some (but probably not all) of these in detail.
As the book's subtitle indicates, all case studies lead to models involving differential equations. Each case begins with a free-form description of an issue and a simple mathematical model. In most cases, further analysis leads to more accurate but more complicated models. Additional explorations and extensions are suggested in exercises which are sometimes open-ended rather than specific questions.
Math 251 (multivariable calculus), Math 221 (linear algebra), Math 225 (differential equations).
This course differs from most mathematics courses in that writing is an essential part of the course. The "deliverable" for each homework problem is a complete and self-contained narrative that describes the problem, the analysis, calculations, conclusions and citations, written in the style of a technical journal article. There will be around 10 such assignments in the semester. The problems will vary in complexity but a typical writeup will be around 5 printed pages.
Writing Advice: No Needless Words
Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline, but that every word tell.
— Strunk & White in "The Elements of Style"
Technical writing is easy with the right tool. LATEX is the computer software of choice for technical writing, especially for articles that contain a lot of mathematics.
LATEX is closer to being a programming language than a word processor. I will devote some class time to LATEX tutorials and expect that you will write your assignments using LATEX.
Once you convince yourself that LATEX is for you, you should consider buying its manual and keeping it within an arm's reach at all times. The manual is:
LATEX: A Document Preparation System by Leslie Lamport.
After you have thoroughly mastered that manual, you may expand your knowledge by reading:
The LATEX Companion (2nd Edition) by Mittelbach, Goossens, Braams, Carlisle and Rowley.
LATEX is an open source software. It may be obtained freely and installed on any computer platform.
Maple™ is a computer software for symbolic computations. For example, Maple can factorize the polynomial 2x3 – 9x2 + x + 12 into (2x – 3) (x – 4) (x+1) and it can figure out that the general solution of the differential equation y'' + y = tan x is y(x) = c1 cos x + c2 sin x – cos x ln(sec x + tan x). (Can you?) In fact, Maple knows just about all the undergraduate and some of the graduate subjects of the standard mathematics curriculum.
As the textbook's subtitle indicates, Maple is used as an analysis aid in case studies. I will devote some class time to Maple tutorials. Probably you will need to use Maple or something equivalent for most of the homework assignments.
UMBC has a campus site license for Maple therefore Maple is available on all university machines.
There are are no exams in this course. Your work will be evaluated solely based on your performance on homework assignments.
I will put homework assignments on this web page as we go along. You may work together on studying and solving problems, however I expect that you will write your solutions and analyses on your own. I don't want to see writeups that are minor variations of others. See The Official UMBC Honors Code at the bottom of this page.
I won't take late homework; please don't ask for exceptions. However one lowest homework grade will be dropped to accommodate unanticipated events.
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By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.
For detailed policies on academic integrity consult:
Author: Rouben Rostamian
