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Math 678 Fall '11

Prerequisites: MATH 677 or equivalent, knowledge of linear algebra and advanced calculus.
Time and venue: MW 4:30-5:45pm Science & Tech I Room 242
Webpage: http://math.gmu.edu/memelian/teaching/Fall11/math678
                 
Instructor: Maria Emelianenko
Email: memelian @ gmu.edu
Office: 226A Science and Tech I
Office hours: TR 4-5pm


 Site contents:  Announcements  Lecture notes  Links  Help info  Anonymous Feedback Form
Announcements
This course provides an introduction to the theory of partial differential equations. Specific topics include Introduction to PDE, transport equation, Laplace's equation, heat equation, wave equation, Sobolev spaces, Sobolev inequalities, second order elliptic equations, linear evolution equations, nonlinear first-order PDE, separation of variables, similarity solutions, transform methods, converting nonlinear PDE into linear PDE, asymptotics, and power series. It will also be demonstrated how these methods can be used in applications.

[08/22/11]  Welcome! Our first meeting is on Monday, Aug. 29. The textbook we are going to use is Lawrence C. Evans: Partial Differential Equations, Graduate Studies in Mathematics, Volume 19, AMS.
If you have time, please try to familiarize yourself with the material by reading the introduction and prepare for the fruitful work this semester. Hope it will be an enjoyable one!

[09/17/11]  Errata to the main textbook can be found on the author's website: [errata]

Lecture notes and homework
Homework and lecture notes will be posted here as the course progresses. Reading assignments and biweekly homework assignments will mostly follow our main text.

Homework:

Homework 1 (due 09/15/11): [hw1.pdf] [hw1sol.pdf]

Homework 2 (due 09/28/11): [hw2.pdf] [hw2sol.pdf]

Homework 3 (due 10/12/11): [hw3.pdf] [hw3sol.pdf]

Homework 4 (due 11/02/11): [hw4.pdf] [hw4sol.pdf]

Homework 5 (due 11/16/11): [hw5.pdf] [hw5sol.pdf]

Homework 6 (due 11/30/11): [hw6.pdf] [hw6sol.pdf]

Final Exam (due 12/14/11): [Final.pdf]

Lectures:

Lecture 1 (08/29/11): [lec1.pdf]

Lecture 2 (08/31/11): [lec2.pdf]

Lecture 3 (09/7/11): [lec3.pdf]

Lecture 4 (09/12/11): [lec4.pdf]

Lecture 5 (09/14/11): [lec5.pdf]

Lecture 6 (09/19/11): [lec6.pdf]

Lecture 7 (09/21/11): [lec7.pdf]

Lecture 8 (09/26/11): [lec8.pdf]

Lecture 9 (09/28/11): [lec9.pdf]

Lecture 10 (10/03/11): [lec10.pdf]

Lecture 11 (10/05/11): [lec11.pdf]

Lecture 12 (10/11/11): [lec12.pdf]

Lecture 13 (10/12/11): [lec13.pdf]

Lecture 14 (10/17/11): [lec14.pdf]

Lecture 15 (10/19/11): [lec15.pdf]

Lecture 16 (10/24/11): [lec16.pdf]

Lecture 17 (10/26/11): [lec17.pdf]

Lecture 18 (10/31/11): [lec18.pdf]

Lecture 19 (11/02/11): [lec19.pdf]

Lecture 20 (11/14/11): [lec20.pdf]

Lecture 21 (11/16/11): [lec21.pdf]

Lecture 22 (11/21/11): [lec22.pdf]

Lecture 23 (11/28/11): [lec23.pdf]

Lecture 24 (11/30/11): [lec24.pdf]

Lecture 25 (12/05/11): [lec25.pdf]

Tentative schedule
  Adobe reader needed to view .pdf files is available here

 Please note that this schedule is subject to change. Make sure you check this site frequently for updates.
1 [08/29/11]
Chapters 1.1, 1.2
 [08/31/11]
2 [09/05/11]
Labor Day, no class
[09/07/11]
3 [09/12/11]

 [09/14/11]
4 [09/19/11]

 [09/21/11]
5 [09/26/11]

 [09/28/11]
6 [10/03/11]

 [10/05/11]
7 [10/10/11]
Columbus Day
Class meets on Tuesday, Oct 11 this week.
 [10/12/11]
8 [10/17/11]

 [10/19/11]
9 [10/24/11]
 [10/26/11]
10 [10/31/11]
 [11/02/11]
11 [11/07/11]

 [11/09/11]
12 [11/14/11]

 [11/16/11]
13 [11/21/11]

 [11/23/11]
Thanksgiving break, no class
14 [11/28/11]

 [11/30/11]
15 [12/05/11]
 [12/07/11]
Final Review


Assessment
Your grade in this course will depend on your performance on homework assignments and a comprehensive take-home final.
- Final exam: 35%
- Homework: 50%
- Participation: 15%

I expect all class participants to abide to the rules and regulations specified in the official GMU Honor code.

Help info and contacts
If you are looking for help, these are some of your options:
  • Try coming to my office hours.
  • If you have conflict with my office hours, talk to me after class or email me, I'll try to make an appointment for you at a different time.
If you have concerns or suggestions that you'd rather leave anonymous, please use the anonymous feedback form. I need to know what you think in order to make the learning process effective, so any feedback is valuable to me.