Finding A Model

Math 55 --- Differential Equations

Model Report as Part of Term Project

The model report (second draft) will count for 20% of the overall grade for your term project in differential equations.

Preliminary Search

This first assignment requires research papers and publications in search of a real-world application of differential equations. There are a number of ways that you can accomplish this goal.

• There is a set of mathematical and physics journals in the CR library. I believe we have copies of The College Mathematics Journal in the stacks. Ask the librarian for help. We also have a limited number of these journals that are available in physical sciences building, room PS116. I will need some help from students in organizing these in order on one of the bookshelves.
• You can search through abstracts of several mathematical journals using Harvey Mudd's Journal Search Tool.
• Harvey Mudd also has posted past issues of its Consortium for Ordinary Differential Equations Experiments (C*ODE*E). This NSF sponsored activity spanned about five years and their are a number of interesting ideas posted in these newsletters.
• There are a number of searchable journals online. Usually, only titles and abstracts are avaialble, but if you see something interesting, you can try the CR library or the periodical stacks at HSU to find the actual article.
  • Mathemtical Gazette
  • Journal of Mathematical Biology
  • Journal of Theoretical Biology.
  • Biometrika

  Look through the periodicals until you find an article of interest containing a real world application of differential equations. The equations could be first or second order differential equations or even a system of first order differential equations. Make sure that you find an article whose topic is appealing---something you find genuinely interesting.

  There are two ways you can approach your search: (1) Just head to the library and start searching (an immense task), or (2) have an idea of what you want to search for before you go to the library. You can browse the internet looking for titles of interest. It is also a good idea to check the bibliographies of differential equations textbooks. Often, a number of interesting articles can be found in these bibligraphies and then you can take these references to the library to search for the full article in the periodical stacks.

  Use the copy machines at the library to make a copy of the article. Note: It costs about 10 cents per page to make copies at the HSU library, so have some change handy. There is also a copy room near the periodical stacks at the HSU library where you can get multiple pages done, handy if you don't have change for the copy machines.

Getting and Installing Latex

• Windows Users
• Download and install Ghostscript. Easy install. Just follow all defaults.
• Download and install GSView. Easy install. Just follow all defaults.
• Download and install Miktex. The least complicated way is to download and run Basic MikTeX 2.7 Installer. Easy install. Just follow all defaults. This minimalist install has tools that will allow you to add packages you need at a later date. Hence the name "Basic".
• Now you need an editor. Download and install WinEdt. WinEdt is shareware. You need to pay a fee of $20 upon which you will get a registration code. You have 30 free days to use the software before it begins popping up annoying messages about registration every few minutes.
• WinEdt is a terrific editor, an investment you won't regret. You can use it for writing programs, html pages, scripts, etc. However, a free alternative (I haven't tried it as I know WinEdt is perfect) might be TeXnicCenter.
• For sophisticated users, there is the free setup described at Claus Dethlefsen's Page. This is very high level use of Emacs, one of the most popular editors used by the open source community of programmers and writers. My suggestion is that most of you should stick to WinEdt as you first start out. Much easier to learn. When you're ready, give this world of Emacs + AucTeX a go.
• Mac OS X Users
• A simple way is to first install MacTeX. Download MacTeX.dmg. This is a huge file, 744MB, so if you don't have a fast connection at home, you might download this at school and transfer to a flash stick. Installing simply requires mounting the dmg by double-clicking, then double-click the MacTeX-2007.mpkg to begin installation. Accept the defaults.
• You now need an editor, so download and install The Latest Version of TeXShop (Mac OS X 10.4 or higher required).
• Linux Users
• Linux systems have tex installed by default.

Writing Your Report

You must prepare your report using the Latex.

1. The first step is to read Writing Scientific Papers in LaTeX. This paper is a bit outdated when it comes to its TeX installations at the end of the article. Better to follow the directions given above. TeX installations are a bit more automatic than they used to be. However, the body of this paper is up-to-date and accurate introduction to writing scientific papers in LaTeX.
2. The next step is to create a folder called ModelProject in your personal directory. Note that you should never use spaces in folder or filenames.
3. Using a text editor, create a file named ModelProject.tex in your Model Project Folder.
4. Place any image files that you might use in your article in your ModelProject folder.
5. Describe the application that you found and carefully explain the differential equation that models the problem situtation. Your explanation should include a description of all variables and parameters in your differential equation and any other information pertinent to the understanding of the problem. Note: Please do not simply state the problem, state the DE, variables and parameters, then leave it at that. Get into the problem. Explain the background and history of the application. Explain how the DE is crafted and how it makes sense. Put some energy into your presentation.
6. Import any graphic images that improve and enhance your presentation.
7. Use references. Label your equations and images, then reference them in writing. For example, "We see in Figure 1 the output of Equation (13)."
8. Make sure that your Model Project includes a bibliography.
9. Due Dates:
   • The first draft of your Model Project is due Friday, February 8. You must include a printout of your report, a printout of the LaTeX source file, and a printout of the article upon which your are basing your report.
     • Between the time the report is assigned and its due dates, you may drop by my office for dissucsion and questions regarding compiling your report. Distance students can submit their files to me via email for critique.
     • I will critique your report and return it to you.
   • The second draft of your Model Project is due Friday, February 29.
     • Between the time the report is assigned and its due dates, you may drop by my office for dissucsion and questions regarding compiling your report. Distance students can submit their files to me via email for critique.
     • I will assign the second draft of your report a grade and return it to you.