|R 9/2||Introduction. Weierstrass existence theorem.|
|T 9/7||Finite dimensional spaces. Riesz lemma. Uniform convexity.|
|R 9/9||Hilbert spaces. Projection. Riesz representation.|
|T 9/14||Sobolev spaces. Strong derivatives.|
|R 9/16||Mollifiers. Du Bois-Reymond lemma. Weak derivatives.|
|T 9/21||Meyers-Serrin theorem. Sobolev lemma. Regularity.|
|R 9/23||Neumann problems. Rellich lemma. Complex scalars.|
|T 9/28||Orthonormal bases.|
|R 9/30||Fourier bases.|
|T 10/5||Sturm-Liouville problems. Resolvent formalism.|
|R 10/7||Hilbert-Schmidt theory.|
|F 10/15||Gelfand triples. Singular Sturm-Liouville problems.|
|T 10/19||Functional calculus. Evolution equations.|
|R 10/21||Seminorms. Local spaces. Tempered distributions. Quasinorms.|
|T 10/26||Hahn-Banach theorem.|
Instructor: Dr. Gantumur Tsogtgerel
Prerequisite: MATH 455 (Honours Analysis 4) or equivalent
Calendar description: Banach and Hilbert spaces, theorems of Hahn-Banach and Banach-Steinhaus, open mapping theorem, closed graph theorem, Fredholm theory, spectral theorem for compact self-adjoint operators, spectral theorem for bounded self-adjoint operators.
Grading: Homework assignments 40% + Midterm Exam 20% + Course project 40%.
Homework: Assigned and graded roughly every other week, through MyCourses.
Midterm: Take-home type, in late Octorber or early November.
Course project: The course project consists of the student reading a paper or monograph on an advanced topic, typing up notes, and perhaps giving a lecture.