Homework PDE Type Suggested due date Worth Book problems Parabolic
30% hw1 Parabolic 9/19/2016 10% hw2 Parabolic
12/1/2016 20% Project Any 12/20/2016 40%
All homework should be emailed to me. Always put MA 5340 in the Subject line of your message. I will send you a reply when I get your mail. If you do not get a reply, I did not get your email. You are responsible for having an email account that can communicate successively with me.
All book problems should be done individually unless explicitly stated in an individual homework assignment. It is acceptable to ask simple questions of other people, but do not collude or work together closely. All dead sources are acceptable, however. Assignments labeled hw... or Project are to be done in assigned groups, not individually.
- Parabolic problems: Ch. 2, pp. 56-61, 2.3, 2.5, and 2.12. Ch. 3, pp. 83-85, 3.3 and 3.5.
- Hyperbolic problems: Ch. 4, pp. 146-150, 4.1, 4.5, and 4.11.
- Theory: Ch. 5, pp. 190-193, 5.1 and 5.7.
- Elliptic problems: Ch. 6, pp. 232-234, 6.2 and 6.7
The English Muffin problem. Each of you received a muffin. Take it home and cook it in a conventional or convective oven.
- Preheat your oven to at least 375 F.
- Do not split your muffin. It must remain intact during the baking and data collection. While your oven is heating up, practice taking the temperature of your muffin on its exterior and inside in the middle.
- Use a meat thermometer that has a wide enough range that includes your kitchen's room temperature, which you need to record.
- Heat the muffin for 10-14 minutes in the oven and note how many minutes.
- Remove your muffin and immediately and every 10 minutes thereafter collect the exterior and center temperatures.
- Plot the exterior and center temperatures against time.Notes:
- If you do not have access to a meat thermometer with a sufficient range (including room temperature), contact me.
- Do no pick up your muffin with your bare hands from the oven. It will be hot and you do not want to burn yourself.
- The data collection should take an hour or more, but not two hours.
- Do not eat your muffin until after you have collected all of your data, which will take considerable time.
- You may work with another class member, but use significantly different heating time or oven temperature. Turn in one set of graphs per person with full details about each muffin. Only turn in one homework per group.
- Consider toasting another English muffin (or an equivalent) to better ensure the integrity of your data source during data collection.
- After data collection is completed you may reheat or toast your muffin. Kippers with capers makes a traditional side dish to your English muffin.What to turn in:
- A single PDF file.
- A description of the room temperature, heating temperature (375 or other), baking time, time interval history, and length of time the whole data collection process took.
- The graph(s).
- All of the class member names involved in your submission.
A computer program. You will use your data from HW1 to initialize the heat equation to model the temperature predictions for what you observed. Use the theta methods for time stepping using theta=0, ½, 1, and the special case of ½-(Δx)2/(12Δt).
- First assume that your muffin is represented by a line of length 3 inches. You know the exterior temperature at x=0 and x=3. You know the center temperature at x=1.5. You know how many minutes you collected data at t=0,10,20,... (or whenever). Discretize the x axis to ensure stability.
- Repeat by modeling the muffin in 2D by adding a 0.5 inch y direction to your muffin (you are looking at the muffin from its side, not its top or bottom).
- To be announced later in the semester.
- Extra credit: model the muffin in full 3D as a cylinder.Notes:
- Write your code in C. You might want to name your codes step1.c, step2.c, ...
- Create a Makefile that works on UNIX(-like) systems. You may/should base it on the class example Makefile.
- You may turn in this assignment as you complete individual Steps. I will give you feedback that may be helpful. Keep extending the report as you complete Steps.What to turn in:
- A zip file (one per group) with a PDF file that describes your results in detail, your complete code, and your Makefile.
- Your report should be divided into sections based on each Step.
Each of you will work in teams of 2-3 on a project due at the end of classes. The proposed projects include the following: