Math 220/CME 303 Homepage, Autumn 2015

Partial Differential Equations of Applied Mathematics

Instructor: András Vasy

Office: 383M

Phone: 723-2226

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

Office hours: Tentative office hours: TBA

Class location: TTh 1:30-2:50pm, Room 380-380C.

Course assistant: Carlos Sing-Long.

E-mail: casinglo "at" stanford.edu

Office hours: TBA

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

• 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 Math 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 9pm on the designated day, which will usually (but not always) be Thursdays. 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 registrar has now confirmed that the final exam will be on Monday, December 7, 3:30-6:30pm.

Lecture Notes

• Introduction to PDE.
• First order scalar semilinear equations.
• First order scalar quasilinear equations.
• Distributions and weak derivatives.
• Second order constant coefficient PDE.
• Properties of solutions of second order PDE.
• The Fourier transform -- basic properties and the inversion formula.
• The Fourier transform -- tempered distributions.
• PDEs and boundaries.
• Duhamel's principle.
• Separation of variables.
• Inner product spaces, symmetric operators, orthogonality.
• Convergence of the Fourier series.
• Solving PDEs.

Problem Sets