Math417 Spring 2009: Partial Differential Equations for Applications
Announcements
1/22: Welcome! The first meeting is on Tuesday January 27.
2/11: Solutions for the 1st and 2nd homework will be posted soon. In the future, we will post the solutions regularly after the collection of homework.
2/19: We reschedule the date for the first Midterm Exam to be
March 10. The covered topics will be the method of separation of variables,
Fourier series and method of eigenfunction expansion (Chapter 1-4, precisely,
1.1-1.5, 2.1-2.5 except 2.5.3, 3.1-3.6, 4.1-4.5). One more word on
homework, homework should due before the lecture on Tuesdays.
3/3: The sample midterm exam is available here. You are assumed to go over your homework. No textbook, lecture notes and calculator will be allowed for the midterm exam. No formulae will be distributed.
3/10: The solution to the midterm 1 is available here.
3/26: Almost no one come to my office on Friday's
office hour, I decided to reschedule the office hour back to Mondays 1-2:45 PM.
In HW6, no students get the full
solution for Exercise 12.5.2, please check
the solution.
4/9: The second midterm is scheduled on April 14, next Tuesday. The
covered topics will be method of characteristics and Sturm-Liouville
eigenvalue problem
(5.1-5.8, 5.10, 12.1-12.5). There will be two problems and
one additional bonus problem of 20 points. The due time for this week's homework
is
rescheduled to next Thursday. You are
assumed to go over your homework for the midterm, and two problems are
essentially contained in the homework.
4/12: There are some typos in the original solution for HW9. If you find some more on the solutions, please notify me.
4/13: I find some more typos in the solution for HW7 (5.3.4c and 5.3.7), thanks Kaitlin for pointing out the typos.
4/14: The solution to the midterm 2 is available here.
4/30: The final is scheduled on Saturday, May 9, 9-12 Noon,
Krieger 304. There will be 5 problem plus 1
bonus problem. I will add one additional office
hour on Friday, May 8, 1-3PM. The review sheet is
also available here (a sample attached).
5/4: The solution to the sample is available here.
Office Hours: Mondays 1:00 PM--2:45 PM in Krieger 222 or by appointment
Lecture: Tuesday and Thursday 12:00 PM--1:15 PM in Krieger 304
Textbook: Applied Partial Differential Equations, Richard Haberman, Fourth Edition
Grader: Longzhi Lin (lzlin@math.jhu.edu) in Krieger 411 (His Math Help Room Schedule is on Friday 11:00AM--1:00PM in Krieger 213)
Lecture Schedule and Assignment
|
Week |
Beginning |
Topics |
Reading |
Homework |
Due Date |
Solutions (Thanks Longzhi) |
|
1 |
Jan 27 |
Derivation Boundary Conditions Separation of Variables |
1.1--1.5 2.1--2.3 |
Prove (1.5.19) or (1.5.22) p28 2.2.4, 2.3.2 d, 2.3.3 b, 2.3.8 |
Feb 3 | HW1 |
|
2 |
Feb 3 |
Heat Equation Laplace Equation |
2.4 2.5.1--2.5.2 |
2.4.4 2.5.1 a d |
Feb 10 | HW2 |
|
3 |
Feb 10 |
Poisson's formula, Maximum principle Well-Posed Problem Fourier series, Convergence |
2.5.4 (Also Strauss 1.5) 3.2--3.3 (Also Strauss 5.4-5.5) |
2.5.14, 2.5.16 3.2.2 a d, 3.3.2 a c |
Feb 17 | HW3 |
|
4 |
Feb 17 |
term by term differentiation method of eigenfunction expansion term by term integration Fourier series: complex form |
3.4 (Strauss 5.6) 3.5--3.6 |
3.4.6, 3.4.11, 3.4.12 3.5.5, 3.5.6, 3.5.7, 3.6.2 |
Feb 24 | HW4 |
|
5 |
Feb 24 |
Wave Equation Characteristics, first order wave equation |
4.1--4.5 12.2, 12.6.1, 12.6.3 |
4.4.3, 4.4.4, 4.4.7 12.2.3, 12.2.4, 12.2.7 |
March 3 | HW5 |
|
6 |
Mar 3 | method of characteristic for one-dimensional wave equation | 12.3-12.5 |
12.3.5, 12.3.6 12.4.1, 12.4.4 a b, 12.5.2 |
Mar 12 | HW6 |
| 7 | Mar 10 |
Midterm Exam I Sturm-Liouville Problem |
5.2--5.3 | 5.3.4 ac, 5.3.5, 5.3.7, 5.3.9 | Mar 31 | HW7 |
| 8 | Spring Vacation | |||||
| 9 | Mar 24 |
Worked example Self-adjoint operator Rayleigh Quotient |
5.4--5.6 |
5.4.1, 5.4.4, 5.4.5,
5.5.1 c d f 5.6.1 a b, 5.6.3 |
Mar 31 | HW8 |
| 10 | Mar 31 |
Worked example, Approximation Properties Robin BC |
5.7, 5.10 5.8 |
5.7.2, 5.10.2 a c, 5.10.3, 5.10.6 5.8.1 b, 5.8.3, 5.8.9 |
Apr 7 | HW9 |
| 11 | Apr 7 | Fourier transform | 10.1--10.4 |
10.3.1, 10.3.3, 10.3.8 10.4.4, 10.4.8 |
Apr 16 | HW10 |
| 12 | Apr 14 |
Midterm Exam II Sine and Cosine transform |
10.5 | 10.5: 1, 4, 9, 12 | Apr 21 | HW11 |
| 13 | Apr 21 |
More Examples, High dimensional Fourier transform Dirac Delta, Green's function |
10.6 9.3.4, 9.5 |
10.6: 1a, 3a, 9, 10, 11 ac 9.3.4 |
Apr 28 | HW12 |
| 14 | Apr 28 |
Poisson Equation Review |
9.5 |
9.5: 5, 14, 15, 16a, 21 | not collected | HW13 |
Midterm Exams: March 10, April 14, in class
(tentative).
Final Exam: May 9, 9-12 Noon, Krieger 304.