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 L^{2} (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) |