web-page: http://www.math.uu.se/~astrombe/FA2006/FA2006.html
Teacher: Andreas Strömbergsson email: firstname.lastname at math dot uu dot se (with "o" in place of "ö").
NEW EXAM 4p: 17 August, 9-14, Polacksbacken. (Those of you who wish to do exam for 6p, please contact me on email to set time for further examination!)
NEW EXAM 4p: 12 June, 9-14, Polacksbacken. (Those of you who wish to do exam for 6p, please contact me on email to set time for further examination!)
Exam 21 April with solutions. Results.
Exam 17 March with solutions. Some results.
Literature:
Kreyszig: Introductory Functional Analysis with Applications,
John Wiley & Sons, New York 1989.
Also: Short text on the spectral theorem for
compact self-adjoint operators.
The following text may also be helpful:
Mathematical statements and proofs.
Curriculum (some small changes are possible!):
For 4 points.
For 6 points.
Homework assignments: These may result in up to 6 bonus points on the exam. In precise terms: x % on the homework assignments give x/10-3 (rounded downwards to nearest integer) bonus points (if 30 <= x < 100). The three assignments, and deadlines for returning, are:
Lectures (all lectures are at Polacksbacken):
Day | Time | Room | Sections | Subject |
---|---|---|---|---|
1: Tue, 24 Jan | 8-10 | 1_113 | Ch. 1 | Introduction, metric spaces |
2: Thu, 26 Jan | 8-10 | 1_113 | Ch. 1 | Metric spaces |
3: Tue, 31 Jan | 13-15 | 1_113 | Ch. 1 | PROBLEM SOLVING (1.2: 4,6,8,10,11. 1.3: 1,6,10,12,13. 1.5: 2,3,10. 1.6: 8,12) |
4: Wed, 1 Feb | 8-10 | 1_113 | Ch. 2 | Normed spaces, Banach spaces |
5: Thu, 2 Feb | 15-17 | 1_113 | Ch. 2 | Normed spaces, Banach spaces |
6: Fri, 3 Feb | 10-12 | 1_113 | Ch. 2 | PROBLEM SOLVING (2.2: 11,15. 2.3: 1,2,3,6,8. 2.4: 1,3,8. 2.5: 1,3,9. 2.6: 13,14,15) |
7: Mon, 6 Feb | 10-12 | 2_244 | Ch. 2 | Normed spaces, Banach spaces |
8: Wed, 8 Feb | 8-10 | 1_113 | Ch. 3 | Inner product spaces, Hilbert spaces |
9: Thu, 9 Feb | 8-10 | 1_113 | Ch. 2,3 | PROBLEM SOLVING (2.7: 6,14. 2.8: 9,11. 2.9: 12. 2.10: 6,13. 3.1: 3,15. 3.2: 8,10. 3.3: 1,6,9. 3.4: 4.) |
10: Fri, 10 Feb | 10-12 | 1_113 | Ch. 3 | Inner product spaces, Hilbert spaces |
11: Mon, 13 Feb | 8-10 | 1_113 | Ch. 3 | Inner product spaces, Hilbert spaces |
12: Wed, 15 Feb | 10-12 | 2_244 | Ch. 3 | PROBLEM SOLVING (3.5: 7,9. 3.6: 6,9,10. 3.9: 6,8,10. 3.10: 4,6,9,15.) |
13: Wed, 15 Feb | 13-15 | 1_113 | Ch. 4 | Fundamental theorems for normed spaces |
14: Fri, 17 Feb | 10-12 | 2_244 | Ch. 4 | Fundamental theorems for normed spaces |
15: Tue, 21 Feb | 8-10 | 1_113 | Ch. 4 | PROBLEM SOLVING (4.2: 5,8. 4.3: 11,13,15. 4.6: 9,10.) |
16: Wed, 22 Feb | 10-12 | 1_113 | Ch. 4 | Fundamental theorems for normed spaces |
17: Fri, 24 Feb | 10-12 | 1_113 | Ch. 4.8-9; 7.1-2 | convergence concepts, spectral theory |
18: Tue, 28 Feb | 8-10 | 1_113 | Ch. 4,7 | PROBLEM SOLVING (4.7: 5,6,14. 4.8: 1,4,5. 4.9: 4,5. 7.2: 5,7,8.) |
** 19: Fri, 3 Mar | 10-12 | 1_113 | Ch. 4.4-5, 4.12-13 | ONLY 6p! More fundamental theorems for normed spaces |
20: Wed, 8 Mar | 13-15 | 1_113 | 8.1 + handout text | Compact operators, spectral theory in Hilbert spaces |
21: Mon, 13 Mar | 8-10 | 1_113 | Ch. 4,8 | PROBLEM SOLVING (8.1: 2,4,6,8. + exercises in handout text + old exams?) |
22: Wed, 15 Mar | 13-15 | 1_113 | REPETITION (solving old exams?) |
For 6p the course continues:
23: Wed, 22 Mar | 8-10 | 2_215 | Ch. 9 | Spectral theory in Hilbert spaces |
24: Wed, 29 Mar | 8-10 | 2_215 | Ch 9,10 | Spectral theory in Hilbert spaces |
25: Wed, 5 Apr | 8-10 | 2_215 | Ch 10.1-3 | Spectral theory in Hilbert spaces. End of lecture 5 April. |
26: Wed, 19 Apr | 8-10 | 2_215 | 4,9,10 | Prespectives (Ch 8,10,11?), or PROBLEM SOLVING
(4.12: 5,7. 4.13: 5,8,15.
9.1: 7,8,9,10. 9.2: 7. 9.5: 8,10. 9.6: 8,9,10,11,12. 9.9: 5,6,7,10.
10.1: 1,2,5,8,9. 10.2: 4,6,9. 10.3: 5,7,10) Or old exam problems? |