Some lecture notes include homework assignments plus solutions.
Lecture notes files.
| 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) |
