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.
Topics: 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.
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.
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%.