Some lecture notes include homework assignments plus solutions.
| LEC # | TOPICS |
|---|---|
| 1 | Linear spaces, metric spaces, normed spaces (PDF) |
| 2 | Linear maps between normed spaces (PDF) |
| 3 | Banach spaces (PDF) |
| 4 | Lebesgue integrability (PDF) |
| 5 | Lebesgue integrable functions form a linear space (PDF) |
| 6 | Null functions (PDF) |
| 7 | Monotonicity, Fatou’s Lemma and Lebesgue dominated convergence (PDF) |
| 8 | Hilbert spaces (PDF) |
| 9 | Baire’s theorem and an application (PDF) |
| 10 | Bessel’s inequality (PDF) |
| 11 | Closed convex sets and minimizing length (PDF) |
| 12 | Compact sets. Weak convergence. Weak compactness (PDF) |
| 13 | Baire’s theorem. Uniform boundedness. Boundedness of weakly convergent sequences (PDF) |
| 14 | Fourier series and L2 (PDF) |
| 15 | Open mapping and closed graph theorems (PDF) |
| 16 | Bounded operators. Unitary operators. Finite rank operators (PDF) |
| 17 | The second test (PDF) |
| 18 | Compact operators (PDF) |
| 19 | Fredholm operators (PDF) |
| 20 | Completeness of the eigenfunctions (PDF) |
| 21 | Dirichlet problem for a real potential on an interval (PDF) |
| 22 | Dirichlet problem (cont.) (PDF) |
| 23 | Harmonic oscillator (PDF) |
| 24 | Completeness of Hermite basis (PDF) |
| 25 | The fourier transform on the line (PDF) |
| 26 | Hahn-Banach and review (PDF) |
