Instructor: Dr. Gantumur Tsogtgerel
Prerequisite: MATH 580 (PDE1), MATH 355 (Honours Analysis 4) or equivalent
Note: If you plan to take this course without taking MATH 580, please consult with the instructor.
The main focus of the course is going to be on nonlinear problems.
Sobolev spaces, the Fourier transform, and functional analytic methods will be heavily used.
The planned topics are
Calendar description: Systems of conservation laws and Riemann invariants. Cauchy-Kowalevskaya theorem, powers series solutions. Distributions and transforms. Weak solutions; introduction to Sobolev spaces with applications. Elliptic equations, Fredholm theory and spectra of elliptic operators. Second order parabolic and hyperbolic equations. Further advanced topics may be included.
There is no required textbook.
The following are recommended.
Homework: Assigned and graded roughly every other week.
Weakly seminars: We will organize weekly seminars on standard results from analysis and geometry, and other stuff related to the course.
Course project: The course project consists of the student reading a paper or monograph on an advanced topic, typing up notes, and giving a lecture.
Grading: Homework assignments 50% + Course project 50%.