Math 182: Partial Differential Equations - Spring 2009
Instructor Information
- Instructor:
Doreen De Leon
- Office: PB 350
- Office telephone: (559) 278-4009
- Office hours: W 3-4:15, Th 2-4, F 1-1:50, or by appointment
Course Information
Announcements
- 02-09-09: In response to the in-class question regarding Example 1
of the Eikonal equation, consider the following. If we know that
a function u(x, y) is constant in the entire (x,y)-plane, then we
know that its gradient is zero because its derivative is 0.
For our problem, where u(x, y) is constant only along the line y = 2x,
the directional derivative in the direction of the line is 0, but the
directional derivative is just the dot product of the gradient of the
function u(x, y) with the vector representing the line.
- 02-25-09: I have been informed that there is an error in problem 1 of
Homework #2. After applying the chain rule to the equation using the
new variables
xi and eta,
the problem should read:
3uxi + (3A + B)ueta = 0.
So the correct choices for A and B should have been A = 1, B = -3.
Proceeding in that way will give you the correct answer for u(x, y),
which is u(x, y) = e-(4-x+3y)2/9
- 02-25-09: There is an error in the example from Friday, 02-20-09. I
will discuss it in class on Friday.
- 03-12-09: Office hours will end at 1:25 on 03-13-09 due to academic
commitments. I apologize for any inconvenience.
- 03-11-09: Office hours on 03-20-09 are cancelled due to academic
responsibilities. An extra hour of office hours will be held on
Tuesday, 3-17-09, at 1:00 p.m. to make up for the loss. I apologize
for any inconvenience.
- 03-25-09: There is a type-o in the problem for Homework #8a).
The problem is for an infinite; the condition
x > 0 was a type-o.
- 03-29-09: There is a type-o in the domain
in the problem for Homework #9a) and in problem 1 for Homework #9b). The
domain should be
0 < x < L, t > 0. I apologize for the
error.
- 04-12-09: Office hours for Thursday, 04-16-09,
are cancelled due to a dental appointment.
- 04-20-09: Please note that I have posted the handout summarizing the
theorems on the Fourier series below.
- 04-22-09: Please note that I made a minor error in class when integrating
the Fourier series of
f(x) from a to
x. The correction is posted below.
I apologize for the error.
- 04-29-09: Hint for Homework #11: 3.5.1 can be found at
Hint.
- 5-04-09: Office hours for Thursday,
May 7, 2009 are cancelled due to academic commitments.
Exam Information
- Midterm I Information
- Midterm I will be given on Wednesday, February 25, 2009,
during the scheduled
class time in the regular classroom.
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Extra office hours: Tuesday, February 24, 2009, 1:30-3:00 p.m.
- Midterm I Topics - posted 02-17-09
- Midterm II Information
- Midterm II will be given on Wednesday, April 1, 2009,
during the scheduled
class time in the regular classroom.
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Midterm II Topics - posted 03-22-09
- Extra office hours: Monday, March 30, 2009, 3-4:30 p.m.
- Midterm III Information
- Midterm II will be given on Wednesday, May 6, 2009,
during the scheduled
class time in the regular classroom.
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Midterm III Topics - revised 04-29-09
- Extra office hours: Tuesday, May 5, 2009, 2-3 p.m.
- Final Exam Information
- The final exam will be given on Monday, May 18, 2009, from
11:00 a.m. - 1:00 p.m. in S2 206
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book. However, you may bring
a one page cheat sheet.
- The exam will be cumulative, and will cover all material covered
on the midterm exams, as well as separation of variables for
elliptic equations
- Extra Office Hours (consultation days): Thursday 2-4
(in PB 350), Friday 11-11:50 (in S2 206), Friday 1:00-1:45 (in PB 350)
Reading Assignments
- 01-23-09: Read Chapter 1 and Sections 2.1-2.2
- 01-25-09: Read Sections 2.3-2.4
- 01-28-09: Read Section 2.5
- 01-30-09: Start reading Section 2.7
- 02-02-09: Finish reading Section 2.7
- 02-04-09: Start reading Section 2.8
- 02-06-09: Finish reading Section 2.8
- 02-09-09: Start reading Section 3.1
- 02-13-09: Finish reading Chapter 3
- 02-27-09: Read Sections 4.1-4.3
- 03-02-09: Read Section 4.4
- 03-13-09: Read Section 4.5
- 03-16-09: Read Sections 5.1-5.2
- 03-20-09: Read Section 5.3
- 03-27-09: Read Sections 3.1-3.2 of Haberman for 04-13-09
- 04-13-09: Read Section 3.3 of Haberman
- 04-15-09: Read Section 3.4 of Haberman
- 04-17-09: Read Section 3.5 of Haberman
- 04-20-09: Read Section 7.1 of text; start reading Section 7.2
- 04-22-09: Finish reading Section 7.2
- 04-24-09: Read Sections 7.3-7.5
- 04-27-09: Read Section 7.7.1
- 04-29-09: Read Section 7.7.2
Homework Assignments
Your homework solutions should follow the format set forth in
Communicating
Mathematics through Homework.
- Homework #1, Due Friday, January 30, 2009 by 11:00 a.m.
- p. 21-22: 1.1(b), 1.2(b) and (c), 1.4(a), 1.5 (Make sure to prove that
ut=p(u)ux, t > 0 has a solution
satisfying u = f(x+p(u)t), where f is
differentiable.), 1.7
- For those without a textbook, I have scanned in the relevant pages:
Ch. 1 problems
- Homework #1 Solutions
- Homework #2, Due Friday, February 6, 2009 by 11:00 a.m.
- Homework #3, Due Friday, February 13, 2009 by 11:00 a.m.
- Homework #4, Due Friday, February 20, 2009 by 11:00 a.m.
- Homework #5, Due Friday, February 27, 2009 by 11:00 a.m.
- Homework #6, Due Friday, March 13, 2009 by 11:00 a.m.
- Homework #7, Due Friday, March 20, 2009 by 11:00 a.m.
- Homework #8, Due Friday, March 27, 2009 by 11:00 a.m.
- Homework #9, Due Friday, April 3, 2009 by 11:00 a.m.
- Homework #9a) -- Please note that there
is a type-o in the problem. The domain should be
0 < x < L, t > 0. I apologize for the error.
- Homework #9b) -- Please note that there
is a type-o in problem 1. The domain should be
0 < x < L, t > 0. I apologize for the error.
- Homework #9 solutions
- Homework #10, Due Friday, April 24, 2009 by 11:00 a.m.
- Homework #11, Due Friday, May 1, 2009 by 11:00 a.m.
- Haberman: 3.4.6, 3.4.12
- Haberman: 3.5.1
- Hint for 3.5.1: Part (a) is basically asking you to integrate
the Fourier series of
f(x) = x. This integral is
given by equation (3.5.6). You just need to write this as a
Fourier series for x2 using some algebra
and a substitution. Then, you get bn.
- Homework 11c)
- Homework #11 solutions
- Homework #12, Due Wednesday, May 13, 2009 by 11:00 a.m.
Handouts and Examples