Week | Date | Sections | |
---|---|---|---|
I. Introduction | |||
1 | 08/29 | 1. Superposition principle | |
08/31 | 2. Solvability conditions | ||
II. Metric Spaces | |||
2 | 09/05 | 1. Basic definitions | 5.1 |
09/07 | 2. Convergence and continuity | 5.2, 6.2 | |
3 | 09/12 | 3. Topological properties | 6.1, 6.4, 6.5, 6.6 |
09/14 | 4. Completeness | 7.1, 7.2, 7.4 | |
4 | 09/19 | No class! | |
09/21 | 5. Separable metric spaces | 6.3 | |
6. Completion of a metric space | 7.4 | ||
5 | 09/26 | No class! | |
09/28 | 7. Compactness | 10.1, 10.2, 10.3, 10.4 | |
III. Linear Spaces | |||
6 | 10/03 | 1. Linear spaces | 13.1, 13.2, 13.3 |
10/05 | 2. Frechet spaces | 17.1, 17.2 | |
3. Banach spaces | 15.1, 15.2 | ||
7 | 10/10 | No class! (Columbus Day) | |
10/12 | 4. Finite-dimensional Banach spaces | ||
8 | 10/17 | 5. Compactness of the unit sphere | |
6. Hilbert spaces | 16.1, 16.2, 16.8, 16.9 | ||
10/19 | 7. Orthonormal sets | 16.3, 16.4, 16.5, 16.6 | |
9 | 10/24 | 8. Orthogonal projections | 16.7 |
10/26 | 9. Superposition principle revisited | ||
IV. Linear Functionals | |||
10 | 10/31 | 1. Continuous linear operators | 18.1, 18.2, 22.1, 22.2 |
11/02 | Midterm Exam | ||
11 | 11/07 | 2. The Banach algebra L(X,X) | 22.3 |
11/09 | 3. Dual spaces | 19.1, 19.2 | |
4. The Hahn-Banach theorem | 14.4, 18.3 | ||
12 | 11/14 | 5. Reflexive spaces | 19.4 |
6. Weak convergence | 20.1, 20.2, 20.3 | ||
7. Weak topology and compactness | 20.4 | ||
V. Linear Operators | |||
11/16 | 1. Inverse operators | 23.1 | |
13 | 11/21 | No class! | |
11/23 | No class! (Thanksgiving) | ||
14 | 11/28 | 2. Adjoint operators | 23.2, 23.3 |
11/30 | 3. Solvability conditions | ||
15 | 12/05 | 4. Spectrum and resolvent | 23.4 |
5. Completely continuous operators | 24.1, 24.2 | ||
12/07 | 6. The Fredholm-Riesz-Schauder theory | 24.3 | |
16 | 12/14 | Final Exam, 4:30-7:15pm |
In addition to the textbook, you might find the following books useful for supplementary reading: