MAT 461 Homework

Fall, 2019

Assignment 2
Due Monday, Sept. 9 (Week 3, day 1)
Read Chapter 1
Do problems 1.2.1, 1.2.5, 1.3.1, 1.3.2, 1.4.1, and 1.4.6 from the textbook (Haberman 4e or 5e).

Assignment 3
Due Monday, Sept. 16 (Week 4, day 1)
1.5.1, 1.5.3, 1.5.11 (So far all the problems in 4e and 5e are the same)
2.2.2, 2.2.3

Assignment 4
Due Monday, Sept 23 (Week 5, day 1)
2.3.1, 2.3.2*, 2.3.3(a-d)*, 2.3.8, 2.3.9.

Hint: in problem 2.3.2(g) Just get an equation for the eigenvalue lambda. You cannot find the eigenvalues in closed form, so don't even try. (You would need to fix a value of L and then find the eigenvalues numerically, so don't even try. If you are interested, here is a Mathematica notebook that can be used to approximate the eigenvalues. This notebook also has a description of a possible class project.)

Directions for problem 2.3.3. In parts (a) and (b) you might be able to find the coefficients, and hence the solution, by inspection. In part (c), you can just leave the coeffient A_n in terms of an integral, as shown in the solution at the back. In part (d) you should do the integral and simplify. The 5th edition has an added part (e) which is not assigned.

Assignment 5
Due Oct 2 (Week 6, day 2)
Non-book problem: Write the vector v = (1, 0, -1) as a linear combination of the orthogonal vectors v₁ = (1, 2, 3), v₂ = (3, 0, -1), and v₃ = (1, -5, 3). See the Appendix to 2.3:
2.4: 1(b-d), 2, 3, 6
2.5: 1(a-d), 2, 3, 7, 8, 10.
Here is a contour map of the solutions to 2.5.1g, with L/W =1 and L/W =3. This is a solution to Laplace's equation on the rectangle with three insulating boundaries, and a specified temperature (a step function) on the bottom boundary.

The first exam is on Friday, Oct. 4. (Week 6, day 3)

Assignment 6
Due Monday, Oct. 14 (Week 8, day 1)
3.2: 1(a, c, e, g), 2(d, e),
3.3: 1, 3(c), 8, 15
Use a computer to plot the series in 3.3.3(c) with different values of the cut off.

Assignment 7
Due Wednesday, Oct. 23 (Week 9, day 2)
3.4: 1, 2, 6
3.5: 2(a), 4
3.6: 1, 2

Due Mon, Oct. 28
Proposals for project. This can be as short as a paragraph, or as long as a few pages.

Assignment 8
Due Wednesday, October 30 (Week 10, Day 2)
4.2: 1
4.3: 1
4.4: 1, 2, 3, 7

Assignment 9
Due Monday, November 4 (Week 11, Day 1)
12.2: 3, 4
12.3: 1, 6

Due Tuesday, Nov. 19 (Week 13), via email
Email me a power point file or pdf of the presentation, or a pdf of the write-up if you plan to use the chalk board. I will look at these and get these back to you for corrections before the presentations to the class.
Presentations will start Friday, Nov. 22

Assignment 10
Due Monday, November 25 (Week 14, Day 1)
5.3: 2, 3, 5
5.4: 3, 6