Math 481: Project 1
The Funnel

Due Monday, February 22

Project 1 is for “warm-up”—I will grade it as a 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-files.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 nine figures in the PDF format. If you have a personal installation of LaTeX on your computer, download proj1-files.zip, unpack, and proceed with LaTeXing. If you are using Overleaf for LaTeX, read the section titled How to upload proj1-files.zip to Overleaf further down on this page.

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 the extended version of the original proj1.tex;
• The figures that go with your 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.

How to upload proj1-files.zip to Overleaf

Here are step-by-step instructions on how to upload proj1-files.zip to Overleaf.

1. Download proj1-files.zip to your computer.
2. In your web browser go to Overleaf's website and log in. Here is what you will see:
   
3. Click on New Project and in the drop-down menu select Upload Project.
   
4. That will pop up a dialogue box through which you should be able to upload proj1-files.zip.
   
5. If the upload is successful, Overleaf's display will change to
   

Now you should be able to edit the LaTeX code, recompile, and view the changes just as we did in our LaTeX workshops. Feel free to change my name as the document's author to yours.

As you edit and extend the document, you will want to upload graphs that you have produced in Maple. To do that, save your Maple graphics in the EPS format, and then in Overleaf's page click on the icon which I have circled in red in the following figure:

In the dialog that pops up, select Upload:

The screen will change to:

Here you should be able to upload the desired graphics files.

How to download and hand in your work

Once you are done with writing, click on the Menu symbol near Overleaf's top-left corner:

The screen will change to:

Click on Source. That will tell your browser to download the entire file collection of your Project #1 as a single zip file to your computer/laptop. To submit your work to me, email me that zip file as an attachment.

That zip file contains only LaTeX code and figures. It does not include the compiled PDF file. To download the PDF, click on the PDF shown in the image above. You will probably want to keep that PDF for your future reference, but do not send it to me.

To close the left panel shown in the figure above, click anywhere outside of that panel in the Overleaf window.

Author: Rouben Rostamian