Partial differential equations I

Organization

Time: Wednesday, 16:00-17:30, room 3120
Group leader: Sławomir Kolasiński
Contact: initial.lastname @ mimuw.edu.pl
Office hours: room 5160 MIM UW, Wednesday 12:15 - 13:45 or upon individual appointment
Please let me know if you want to come (via e-mail) because I might not be in my office.

Rules of getting credit:

We plan to organize two common (the same for both groups) mid-term exams. Each mid-term counts as 40% of the overall credit. Additional 20% is my subjective rating. This 20% will include evaluation of student's activity and homework. I plan to give about 3-5 series of homework during the semester.

Some problems worth solving just for practice:

• There is a script prepared by MIM UW lecturers with lots of example problems.
• First order equations. The method of characteristics and first integrals.
• Gauss-Green theorem, i.e. the art of integration by parts.
• Wave equation.
• Canonical forms.
• Example solutions using separation of variables.
• Energy methods. Uniqueness of solutions.
• Harmonic functions
• The Green representation formula
• Weak derivatives and the Sobolev spaces
• The Lax-Milgram theorem

Homework:

• Homework 1
• Homework 2