Hint added for Problem 9.5.
Problem set 9 up.
1 May, 2015: Some notes for lecture on 30 April added (in new section) to Chapter 4, not yet complete.
Lecture 30 April: The harmonic oscillator.
More added to the notes, Chapter 4, on Fourier transform.
Lecture 28 April, Fourier Inversion formula. There is a NEW section 8 in Chapter 4 of the notes below covering much of the lecture last Thursday and today.
Lecture 23 April: Fourier Transform, read Notes Chap 4 Sect 7.
Corrections in P4 and P5 of Problems 8 -- eigenvalues wrong. Thanks Xun and Jonathan.
Solutions to Test2-pre up.
Everyone should have their Test2 and PS7 returned by now -- if not let me know.
Problem set 8 up -- note due date is 25 April.
Lecture 16 April: Dirichlet problem. Notes Chap 4 Sect 2.
Lecture 14 April: Functional calculus, Fredholm operators. Notes Chap 3 Sects 19-21.
9 April, Test 2.
Lecture 7 April: Self-adjoint operators, spectral theorem for compact self-adjoint operators. Read Chap 3, Sects 17,18 maybe 19.
Lecture 2 April: Open Mapping Theorem, Closed Graph Theorem, Spectrum and resolvent set for a bounded operator.
30 March, 2015: Questions for Test2 below.
Lecture 31 March: Completeness of the Fourier basis, Fourier series. Read Chap 4 Sect 1.
Misdirection fixed in Problems7, thanks Panos.
29 March, 2015: Problems7 up.
Having heard from several of you (even if I did not reply yet!) I have decided to postpone the second test for a week and hold it on 9 April. I will put questions up (and a problem set for this week) tomorrow, Sunday. If anyone is seriously inconvenienced by this, they can have a take-home version of the test (different selection) overnight for 2 April, self-policed but only 80 minutes as for the in-class version. Sorry for the mess.
Acknowledgement of receipt of homework 6 will have to wait until tomorrow -- so it is still okay if you submit/resubmit.
Due to poor timing, I am thinking of simply cancelling the test scheduled for 2 April -- since moving it later seems unfair. The only downside of this I can see is that it will shift the balance of grades a bit. If anyone has a strong view on this, please let me know ASAP!
Yet another typo in Problem 6.4 that I missed despite Xun pointing it out.
Another typo, in Problem 6.3, corrected -- Thank you Xun.
For Lectures this week -- Chap 2 Sects 13, 14, 15, Chap 1 Sects 8,9.
15 March, 2015: New version of Problem set 6 -- with a hint (really a remark) for Problem 6.1
14 March, 2015: Problem set 6 up; don't leave it too late to ask questions since I will be travelling in part of Spring Break.
14 March, 2015: You should have acknowledgment for PS5 by now.
For Lecture 10: Compact sets. Chap 2 11-13 (start of).
Typo in Problem 5.6 corrected, thank you James.
You should have your graded Test and PS4 back by now. If you have any questions, please ask!
For Lecture 9:Riesz Representation Theorem, read Chap 2 sects 8 -- 11.
6 March, 2015: Problem set 5 up.
Problems from which those on the test on Thursday will be selected -- see Test1-pre.pdf below.
Solutions to Problem sets 3 and 4 -- the latter sent our earlier.
For Lecture 7, 3 March, 2015: Read Chap 3 Sects 3-7.
Corrected version of Problem set 4, thanks to Daniel for spotting the typos.
For Lecture 6, 26 February, 2015, Chap 2 Sect 10, Chap 3 Sects 1 and 2.
Problem set 4 finally up.
For Lecture 5, 24 February, read Chap 1 Sect 5 (seminorms), Chap2 Sects 5 and 6.
Sorry about the delay with Problem set 4, should be up Monday evening, 23 Feb.
Note Friday office hour above.
Corrected Problem set 3, 1:30PM, 17 February, 2015
For lecture 4, read Chap 2 Sects 3 (the integral) and 4. You might also want to recall the material at the end of Rudin Chap 3 on rearrangement of series.
Problem set 3 is up.
For Lecture 3, read Chap 2 Sects 1 and 2.
Problem set 2 is up.
Problem set 1 submission closed -- late from now on.
Special Office Hour Friday 2-3PM, 6th Feb, E17-340.
Note there is a problem set due at the end of this week!