Math 481: Project 1
The Funnel

Due Wednesday, September 25

Project 1 is for “warm-up”—I will assign it a grade for feedback to you but it won't count toward the overall course grade.

Animation of the emptying of a funnel

I solved the differential equation for the height h(t) in a funnel (with inflow rate set to zero), produced the animation in Maple, exported it as a multiframe GIF image, and further processed the image using ImageMagick's command-line tools.

Note the accelerated drop of the water level near the end and the corresponding steepening of the slope in the graph of h(t).

Height versus time in a funnel

What to do

I have written a good part of Project 1's report. Sections 1–4 are complete but sections 5 and 6 only say what needs to be done, without doing them. It is your job to complete them. The zip archive proj1.zip contains the files pertaining to my part of the writeup. These consist of the LaTeX file proj1.tex, the bibliography file proj1.bib, and seven figures in the PNG format. If you have a personal installation of LaTeX on your computer, download proj1.zip, unpack, and proceed with LaTeXing. [The file unpacks into a folder named proj1.] If you are using Overleaf for LaTeX, you need to start a New Project there and upload the zip file to that project. Overleaf will unpack the zip file on its own.

In either case, edit proj1.tex, complete sections 5 and 6, and add your own figures.

When done, send your report to me at rostamian@umbc.edu. I need:

• Your LaTeX source code, proj1.tex, which is your extended version of the original proj1.tex;
• The figures that you have added to the document;
• The bibliography file proj1.bib.

I don't need your proj1.pdf—I will compile your files on my machine and generate the proj1.pdf myself.

Beware that the LaTeX code in proj1.tex goes far beyond what I have introduced in class. Don't expect to understand everything there. Sections 5 and 6 that you are going to add, however, require nothing beyond the basic concepts that we have already learned.

Important!

Don't leave things to the last moment—the first project tends to hit more snags than you may anticipate. Start early and give yourself a few days of slack to cope with the issues that may arise along the way.

Helpful Reminder

Does your Maple interface look different from mine? Read and follow the instructions in Configuring Maple to fix.