Introduction to Microlocal Analysis: 18.157 -- Spring 2014

• Lectures in E17-133, Tuesday and Thursdays 11-12:30PM.
• Office hour in E17-340 maybe.
• Please ask questions!
• Comments and remarks:
  • There will be no class today, 15 April, 2014. Sorry about that.
  • I did not get anyone to speak on 1 April, so there will be no lecutre until Ting Zhou speaks on 3 April.
  • Note added to Problems5 with changing version -- I assume no one saw it in the meantime.
  • Ting Zhou will give a lecture on Thursday 3 April.
  • Problems 5 up, 12 March, 2014.
  • Another typo in Problems4 eqn(4) spotted by Saul.
  • Some typos fixed in Problems4 -- eqn (4) -- thanks Saul.
  • Problems4 -- hastily written, probably too long and insufficiently explained but have a go and let me know!
  • Corrections to Problems3 from Saul -- eq (2) and a missing R in No8. Don't quite know what happened in No7 but I did not change it.
  • Problems3 up, 27 February, 2014.
  • Solutions to (revised) Problems2 up, 24 February, 2014.
  • 23 February, 2014: More corrections to Problems 2 -- sign of eigenvalue, thanks Felipe.
  • 23 February 2014: Second problem corrected and then corrected again -- it was unintentionally trivial, thanks Julian.
• Old remarks
• Lecture schedule and informal notes -- this describes what I expect to talk about/did talk about with pointers for more details.
  1. • Lecture 1: 4 February.
     • Lecture1H Handwritten notes, probably unreadable.
  2. Lecture 2: 6 February.
  3. Lecture 3: 11 February.
  4. Lecture 4: 13 February.
     18 February is an MIT Monday.
  5. Lecture 5: 20 February.
  6. Lecture 6: 25 February.
  7. Lecture 7: 27 February.
  8. Lecture 8: 4 March.
  9. Lecture 9: 6 March.
  10. Lecture 10: 11 March.
  11. Lecture 11: 13 March.
  12. Lecture 12: 18 March.
  13. Lecture 13: 20 March.
  14. Lecture 14: 1 April
  15. Lecture 15: 3 April.
  16. Lecture 16: 8 April.
  17. Lecture 17: 10 April.
  18. Lecture 18: 15 April.
  19. Lecture 19: 17 April.
  20. Lecture 20: 24 April.
  21. Lecture 21: 29 April.
  22. Lecture 22: 1 May.
  23. Lecture 23: 6 May.
  24. Lecture 24: 8 May.
  25. Lecture 25: 13 May.
  26. Lecture 26: 15 May.
• Outline of course: I will follow various parts of these notes from earlier courses and add a few new pieces as I go along.
  Notes
  1. Basic theory of pseudodifferential operators on Euclidean space -- 4 lectures.
  2. Elliptic operators on manifolds -- Hodge theory.
  3. Semiclassical operators.
  4. Manifolds with boundary.
  5. Conormal distributions.
  6. Lagrangian distributions.
• References (besides the notes).
  • Volume 3 of Hörmander's 4 volume work, gives you some introduction.
• Tests and Exams. There will be none.
• Grades: For undergraduate if there are any. In fact there seem to be:
• Problem sets.
  1. Problem set 1: 7 February Will grade 7AM Monday 10 February,
     v2: Typos fixed thanks to Felipe.
     Problem set 1 solutions
  2. Problem set 2: 20 February, 2014 Will grade 7AM Monday 24 February
     v2 Problem 2 corrected by making the forcing term have compact support.
     v3 it was still trivial.
     v4 sign of eigenvalue changed
     Problem set 2 Solutions 24 February, 2014.
  Problem set 3v2/a> Will grade 7AM Monday 3 March.
  v2 2 March, 2014 -- typos.
• Problem set 4 v3 Will grade 7AM Monday 10 March,
  v2 7 March, 2014 -- typos
  v3 another typo in (4).
• Problem set 5 Due Thursday 20 March