MATH 412-502

MATH 412-502 "Theory of Partial Differential Equations", Fall 2010

Instructor: Dr G.Berkolaiko, office: Blocker 625c, phone: 845-1924, email: berko AT math.tamu.edu
Lectures: TR 9:35-10:50 in BLOC 164
Office hours: W 1-2pm and by appointment
Course description (first day handout)
FAQ

HW 1

1.3.1; 1.4.1bfg, 3, 10; 1.5.5, 8, 11, 14; some solutions

HW 2

2.2.4; 2.3.1ace, 2a, 3ab, 5, 7 ; 2.4.3, 4, 6; some solutions

HW 3

2.5.1b, 3, 5ad, 7a, 12 (integrate by parts), 14, 15d; some solutions

HW 4

3.2.1ac, 4; 3.3.4, 15; 3.4.1, 2, 3, 9, 12 some solutions

HW 5

These questions in addition to 4.2.1, 2; some solutions

HW 6

4.4.8-12; some solutions

HW 7

12.2.3, 4, 5acd; 12.3.5; 12.4.1, 2; derive and explain the solution for a semi-infinite string with a free BC at x=0; some solutions

HW 8

10.3.1, 5-8, 18*; some solutions

HW 9

10.4.3-5; some solutions

HW 10

Prove that the Wronskian of two solutions of the homogeneous Sturm-Liouville problem d/dx[p(x) du/dx] + q(x)u = 0 satisfies W(u_1,u_2) = const / p(x). Hint: differentiate p(x)W and prove it is zero.
Solve t^2y'' - t(t+2)y'+(t+2)y=2t^3, if homogeneous equation has solutions y_1 = t and y_2=te^t.
Solve ty'' - (1+t)y' + y = t^2 e^{2t}, if homogeneous equation has a solution y_1 = 1+t.

HW 11

9.2.3; 9.3.1, 2, 4cd, 5; some solutions

Material covered
We covered, with a varying degree of detail the following sections, grouped by their "theme" (stars mark the section we studied in least detail): Derivation of main equations: 1.1-1.4, 4.1-4.3 Eigenfunction expansion: 2.1-2.5, 3.1-3.5, 4.2-4.4, 7.5, 8.1-8.3 (generalizes 2.1-2.4), 8.4, 9.2 (similar to 8.3 but with different emphasis) Green's function: 9.1-9.3, 9.5, 11.2, 11.3 Fourier transform: 10.1-10.5, 10.6.1, 10.6.3, 10.6.5 Method of characteristics: 12.1-12.5
Some comments: Derivation of the equations is helpful for understanding but will not be on the test. All other "themes" will be covered. Eigenfunction expansion is pretty fully described in 8.1-8.4 and 9.2. Preceeding sections cover parts of the method in the simpler cases. Fourier transform method can be viewed as a "continuous" eigenfunction expansion (but has to be studied in its own right). Review the homework! Additional exercises: 8.3.1, 9.2.1
The final will take place in our regular class room at 12:30-2:30 on Friday 10th of December. Bring your own formula sheets and paper.
9 Dec 2010
Review
We will have a review meeting on Wednesday at 3pm in Bloc 612. See you there!
6 Dec 2010
Midterm
Our midterm will take place on Tue, Oct 19th in the regular class time / place. Everyone is allowed A4 sheet (2 sides) of paper with formulas. I reserve the right to confiscate sheets containing solutions to entire problems. Study hard! Do well!
14 Oct 2010

This file was last modified on Wednesday, 10-Jan-2024 15:57:57 CST.