MA 5340, Fall 2016 (Comp Methods II)
Professor Craig C. Douglas
 
Monday / Wednesday 2:10-3:25, Ross Hall 241
Office hours: T/R 11:00-12:00, W 1:00-2:00, Ross Hall 227
 
http://www.mgnet.org/~douglas/Classes/na-sc
 

 

Homework

Homework PDE Type Suggested due date Worth
Book problems Parabolic
Hyperbolic
Theory
Elliptic
10/4/2016
11/3/2016
11/17/2016
10/18/2016
30%
hw1 Parabolic 9/19/2016 10%
hw2 Parabolic
   Step 1
   Step 2
   Step 3
   Step 4
12/1/2016
20%
Project Any 12/20/2016 40%

Homework

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.

Book Problems

HW1

The English Muffin problem. Each of you received a muffin. Take it home and cook it in a conventional or convective oven.

  1. Preheat your oven to at least 375 F.
  2. 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.
  3. Use a meat thermometer that has a wide enough range that includes your kitchen's room temperature, which you need to record.
  4. Heat the muffin for 10-14 minutes in the oven and note how many minutes.
  5. Remove your muffin and immediately and every 10 minutes thereafter collect the exterior and center temperatures.
  6. Plot the exterior and center temperatures against time.
Notes:
What to turn in:

HW2

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).

  1. 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.
  2. 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).
  3. To be announced later in the semester.
  4. Extra credit: model the muffin in full 3D as a cylinder.
Notes:
What to turn in:

Project

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:

Cheers,
Craig C. Douglas

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