Office: 383M

Phone: 723-2226

E-mail: andras "at" math.stanford.edu

Office hours: T3-4:45pm, W 10:45am-12noon. Exception: Wednesday, Nov 14, office hour cancelled. Instead: Tuesday, Nov 13 office hour runs 3-5pm, and special office hour on Thursday morning 9:15-10:15am.

Class location: TTh 1:30-2:50pm, Room Herrin T175.

Course assistant: Rahul Sarkar

E-mail: rsarkar "at" stanford.edu

Tentative office hours: MWTh 4-6pm, Room Herrin T175, with the exception of Oct 15-19, when the times are M 4-7pm, T11am-12noon, T5-7pm, Room TBA, tentatively Huang basement in front of ICME.

Textbook: due to the availability of lecture notes, the following are all `recommended'.

- The instructor's `Partial Differential Equations: An accessible route through theory and applications' is a slightly updated and somewhat expanded version of the earlier manuscript chapters, listed below.
- Strauss' `Partial Differential Equations: An introduction' covers most topics, but the course is at a higher level, especially regarding first order PDE's, which is the first major topic covered, as well as distributions and the Fourier transform.
- Evans' `Partial Differential Equations' is a more advanced text, and it covers course topics not dealt with in Strauss' book.
- Pinchover and Rubinstein's `An introduction to partial differential equations'. This is a fairly good match for the level of difficulty of the course, though does not necessarily cover the same topics/the same way.
- All of these, as well as John's `Partial Differential Equations' will be on reserve at the Engineering (Terman) library.

The running syllabus is here.

Grading policy: The grade will be based on the weekly homework (25%), on the in-class midterm exam (30%) and on the in-class (i.e. not take-home, to take place during finals week, as designated by the registrar) final exam (45%).

The homework will be due in class or in the instructor's mailbox by 9am on the designated day, which will usually (but not always) be Fridays. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself. This ensures that, apart from satisfying a requirement for this class, you can solve the similar problems that are likely to arise on the exams.

The exam is 75 minutes. Please arrive a few minutes early (so by 1:25) so that we can start on time. The exam is closed book, notes, computers, etc.

To prepare for the exam, first read through the lecture notes, then go through the problem sets, and finally attempt the practice exam (which was an actual exam in 2009).

There is a practice midterm with solutions.

The mean and median were about 62/100. There are no letter grades on the midterm; it is the total score for the course that determines the course letter grade. As a rough guide to help you gauge what the midterm means for the course, scores in the 90s might correspond to an A+, from the high 70s to the 80s an A, the rest of the 70s to A- or B+, the mid 50s-60s a B, mid 40s-low 50s a B-, upper 30s-low 40s a C+, low-mid 30s C, upper 20s C- or D+, rest of the 20s D.

The exam and solutions are available!

The mean and median were about 120/150. There are no letter grades on the final; it is the total score for the course that determines the course letter grade.

The exam covers all the material we went through this quarter with an emphasis on the second half of the quarter. Please arrive a few minutes early (so by 12:10) so that we can start on time. The exam is closed book, notes, computers, etc.

To prepare for the exam, first read through the lecture notes, then go through the problem sets, and finally attempt the practice exam (which was an actual exam in 2009).

There is a practice final with solutions.

- 1. Introduction to PDE.
- 2. Where do PDE come from?
- 3. First order scalar semilinear equations.
- 4. First order scalar quasilinear equations.
- 5. Distributions and weak derivatives.
- 6. Second order constant coefficient PDE.
- 7. Properties of solutions of second order PDE.
- 8. The Fourier transform -- basic properties and the inversion formula.
- 9. The Fourier transform -- tempered distributions.
- 10. PDEs and boundaries.
- 11. Duhamel's principle.
- 12. Separation of variables.
- 13. Inner product spaces, symmetric operators, orthogonality.
- 14. Convergence of the Fourier series.
- 17. Solving PDEs.

- Problem Set 1, due Friday, October 5, at 9am. Solutions.
- Problem Set 2, due Friday, October 12, at 9am. Problem Set 2 is extended to Tuesday, October 16, 9am. Solutions.
- Problem Set 3, due Friday, October 19, at 9am. Problem Set 3 is extended to Tuesday, October 23, 9am. Solutions
- Problem Set 4, due Friday, October 26. Solutions
- Problem Set 5, due Wednesday, October 31. However, solutions will NOT be posted right away. If you hand in the solution in person, on Wednesday morning before NOON, in Room 383M, you can get a hard copy solution, which you will be asked not to share. Conversely, if you are not handing it on Wednesday, you can hand it in until Tuesday, Nov 6, at 10am, but you are NOT allowed to look at the printed solutions; solutions will be posted after this. This should be amenable to both those of you who want a Wednesday due date and those who do not. Solutions
- Problem Set 6, due Thursday, November 15. Solutions
- Problem Set 7, due Friday, November 30. Solutions
- Problem Set 8, due Thursday, December 6. Solutions
- Problem Set 8, Part II, do not hand in! (Practice on last week's material.) Solutions