Graduate Analysis: 18.155 -- Fall 2011

• Lectures in 2-146, Tuesday and Thursdays 11-12:30PM.
• Office hour in 2-174. By consensus Wednesday 3PM.
• Please ask questions!
• Comments and remarks:
  • 5 December, 2011: New version of Michael A.'s notes.
  • 28 November, 2011: Some more detail on the final Assignment added. Ask if you need more or want to do one of the problems not discussed in detail (because nobody asked).
  • 23 November, 2011: Michael A's notes added below.
  • 15 November, 2011: V6 of Problem9, a new record!
  • Further correction to Problems 9, namely question 3. Also a typo in Q5 -- v
  • Revision of last problem in Problems 9.
  • 14 November, 2011: Added a couple more possible projects -- wave equation and harmonic oscillator. I scratched Problem set 11.
  • Problems 9 up, Monday morning 14 November, 2011. If you need to submit them later than the due date on Friday you can have up to Sunday midnight, but I will likely grade the `late' ones.
  • Brief notes for Lecture 16 up.
• Old remarks
• Lecture schedule and informal notes:
  1. Lecture 1: 8 September.
  2. Lecture 2: 13 September.
  3. Lecture 3: 15 September.
  4. Lecture 4: 20 September.
  5. Lecture 5v2: 22 September.
  6. Lecture 6: 27 September.
  7. Lecture 7: 29 September.
  8. Lecture 8: 4 October.
  9. Lecture 9: 6 October.
     (11 October, no lecture.)
  10. Lecture 10v2: 13 October.
  11. Lecture 11: 18 October.
  12. Lecture 12: 20 October.
  13. Lecture 13: 25 October.
  14. 27 October. I will be away, so there will be no lecture.
  15. Lecture 14: 1 November.
  16. Lecture 15: 3 November.
  17. Lecture 16: 8 November. Brief notes only
  18. Lecture 17: 10 November.
  19. Lecture 18: 15 November.
  20. Lecture 19: 17 November.
  21. Lecture 20v2: 22 November.
      (24 November, no lecture.)
  22. Lecture 21: 29 November.
  23. Lecture 22: 1 December.
  24. Lecture 23: 6 December.
  25. Lecture 24: 8 December.
  26. Lecture 25: 13 December. (probably no lecture)
• Notes-from-Michael-A v2
• 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.
• 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 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 Nikhil Savale, email nikhilas AT MIT.EDU
• Problem sets. I want all problem sets to be submitted to me electronically at the email address abov. 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. 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 solutions to all problems but are permitted, indeed encouraged, to discuss it with others, ask me and/or read whatever you want.
• Due Friday 9 September:Diagnostic Test. This will NOT be counted towards homework grades. I have to decide how much time to devote to measure theory and make a few other similar decisions. This is intended to help you and me so please take the time to go through it.
• Problems and Assignments:-
  • Problems1v4 (10 September, 2011) due 16 September, 2011.
    Done a little in haste since I changed this after looking at the diagnostic tests; further minor corrections which probably would not have confused anyone.
  • Problems2v3 (17 September, 2011) due 23 September, 2011.
    Small typo in problem 1 fixed thanks to Darij Grinberg.
    22 September, 2011: And another one. The rectangles are supposed to be upper-open.
  • Problems3v2 (22 September, 2011) due 30 September, 2011.
    24 September, 2011: Typos in Problems 1 and 2 fixed, thanks Wenzhe.
  • Problems4v8 (6 October, 2011) due 7 October, 2011.
    Indexing of sequences corrected.
    Major changes, thanks Jonathan for pointing out the problems.
    TeX typo fixed.
    Signs fixed, constants and typos thanks to Jonathan and Wenzhe.
    Substantial hint added for Question 4 -- weak formulation of the norm; further expanded.
  • Problems5v3 (12 October, 2011) due 14 October, 2011.
    Hint on Problem 4 expanded a bit.
    Hint on Problem 4 clarified.
  • Problems6v4 (18 October, 2011) due 21 October, 2011.
    Added some Hints/Remarks to suggest what I would like to see.
    Important correction regarding the exhaustion -- the condition was too weak.
  • Assignment1v2 due by the very end of October, 2011. However, you might choose to submit a version earlier to get a reaction from me. Note that I will be out of town from Tuesday 25th (after lecture) to Sunday 30th but still likely to respond to email.
  • Problems8 due 11 November, 2011.
  • Problems9v6(14 November, 2011) due 18 November, 2011.
    Last problem changed -- Jonathan spotted the mess. Perhaps I could have sorted out the old algebra but instead I changed the operators under discussion. I will add some hints later.
    Further egregious error found by Jonathan, this time in question 3.
    Another typo in Q5 noted by Michael A., I hope it is right now ...
    V6 -- formula at end of hint on Q5 changed (corrected maybe). Treat A as a constant to understand it.
  • Assignment2v5 due by the very end of November, 2011
    Modified 10 November, 2011 -- I am working on fleshing out the questions.
    28 November, 2011: More detail added to various of the questions.