Graduate Analysis: 18.155 -- Fall 2013
- Lectures in E17-133, Tuesday and Thursdays 11-12:30PM.
- Office hour in E17-340. Wednesdays 2-3PM
- Please ask questions!
- Comments and remarks:
- 22 December, 2013: First part of Lecture21.
- 13 December, 2013: Lecture have finished and grades will go in today. However I will continue to upgrade some of the notes for the last 7 or so lectures -- these have `N' in the names.
- Old remarks
- Lecture schedule and informal notes (i.e. the notes from which I give the lectures):
- Lecture 1: 5 September.
- Lecture 2: 10 September.
- Lecture 3: 12 September.
- Lecture 4: 17 September.
- Lecture 5: 19 September. (Added a little 19 September, 2013)
- Lecture 6: 24 September.
- Lecture 7: 26 September.
- Lecture 8: 1 October.
- Lecture 9: 3 October.
- Lecture 10: 8 October. Brief Only.
- Lecture 11: 10 October. Somewhat expanded.
(15 October, no lecture.)
- Lecture 12: 17 October.
I will be away, but Kiril Datchev has agreed to entertain you!
- Lecture 13: 22 October (trimmed, 23 October, 2013)
- Lecture 14: 24 October. (v3 a little more added 24 October, 2013; link fixed thanks to Chen)
- Lecture 15: 29 October. v2 -- trimmed
- Lecture 16: 31 October.
- Lecture 17: 5 November. v4 -- proof of diffeomorphism invariance of Sobolev spaces added, v3 15 November, 2013.
- Lecture 18: 7 November. N1 -- more on smoothly bounded domains.
v2 18 November, 2013; in part 16 November, 2013.
- Lecture 19: 12 November. N1 14 December, 2013 somewhat rewritten; v3 more at end; v2 More added at beginning, 12 November, 2013.
- Lecture: 14 November. Cancelled.
- Lecture 20: 19 November. N1 15 December, 2013 -- smooth functions on the boundary of a smoothly bounded domain.
- Lecture 21: 21 November. N1 22 December, 2013.
- Lecture 22: 26 December. v3 comment on regularity after the commutation lemma -- still much missing.
(28 November, Thanksgiving -- no lecture!)
- Lecture 23: 3 December. Larry Guth will talk at the end about his plans for 18.156 in the Spring.
- Lecture 24: 5 December. 4 December, 2013: v4 -- small adjustments and typos fixed.
- Lecture 25: 10 December.
- Outline of course:
- Old Notes from an earlier version of this course. Once I decide how much measure theory to do, I will rearrange these to be closer to the present structure. The same but broken into Chapters.
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- References (besides the notes). For the early part of the course I suggest:
- Volume 1 of Hörmander's 4 volume work,
- The little book of Friedlander and Joshi (Cambridge University Press) is also good.
- There is a fairly new book by Duistermaat and Kalka which looks pretty good.
- Tests and Exams. There will be none. But there will be two assignments in the Problem sets which will need some time and effort.
- Grades: Will therefore be based around 50/50 on Problem sets and the larger Assignments.
- Our grader is Qiang Guang
- Problem sets. I want all problem sets to be submitted to me electronically at the email address above. It is fine if you hand-write the solutions (clearly) and scan them. All homework will be due on Fridays at Midnight in the sense that it should be emailed by then (in practice I will not get to it until Saturday morning). If it is late I will deduct an as-yet-undetermined-percentage of the marks, depending on circumstances but late homework WILL be graded. You should write out your own answers to all problems but are permitted, indeed encouraged, to discuss it with others, ask me and/or read whatever you want -- but please then think it all through for yourself and formulate your own solution.
- Problems and Assignments note versions and date (last modified):-
- Diagnostic Test. (5 September, 2013) due Friday 6 September -- by email as everything else.
This will NOT be counted towards homework grades. I will use responses to this to decide how much time to devote to various things. This is intended to help you and me so please take the time to go through it -- you can also ask me about it of course.
- Problems1S Solutions to Problems1 -- 14 September, 2013.
- Problems2S Solutions to Problems2 -- 21 September, 2013.
- Problems3 20 September, 2013, due 27 September, 2013.
- Problems4 v3 2 October, 2013 expanded hints, due 5 October, 2013.
- Problems5 4 October, 2013 -- is the first assignment, due 19 October.
- Problems6 P2 changed 22 October, 2013, due 25 October, 2013.
- Problems7 v4 -- some notes on P4 added,
v3 missing inverses inserted, thanks Evgeni, 27 October, 2013;
v2 typo fixed, thanks Chen, due 1 November, 2013.
- Problems8 v2 -- a couple of points clarified, thanks Ewain, Nina and Evgeni; due 8 November, 2013.
- Problems9 v3 20 November, 2013: more words added to first problem; v2 11 November, 2013 corrected inequality, thanks Nina, due 22 November, 2013.
- Assignment2 due 6 December, 2013: v1, 19 November, 2013