Introduction to microlocal analysis: 18.157 (`Spring' 2000)
General information
Here is a description of the intended course
Announcement.
If you want to print it out, here it is as a postscript file announce.ps.

Lectures
Lectures are in 2255, Tuesdays and Thursdays 12:30PM. Also there are some additional (optional) lectures on Mondays, 56PM, in the same room.
 1st February, 2000: Schwartz test functions, tempered distributions, Schwartz representation theorem, Schwartz kernel theorem. Sections 1.11.5.
 3rd February, 2000: Fourier transform, Fourier inversion formula. Sections 1.61.8.
 8th February, 2000: Symbols, density, products, ellipticity. Sections 2.1.
 10th February, 2000: Pseudodifferential operators, action on Schwartz' space.
 15th February, 2000: Reduction theorem.
 17th February, 2000: Product of pseudodifferential operators.
 24th February, 2000: Ellipticity, L^2 boundedness started.
 28th February, 2000: L^2 boundedness, Sobolev spaces.
 29th February, 2000: Polyhomogeneity, radial compactification, isotropic algebra.
 2nd March, 2000: Isotropic algebra.
 6th March, 2000: Isotropic composition.
 7th March, 2000: Residual algebra and Fredholm property of isotropic elliptic operators.
 9th March, 2000: The harmonic oscillator.
 13th March, 2000: Traces, determinants and forms.
 14th March, 2000: Fredholm determinant, analytic Fredholm theory.
Spring hiatus
 13th April, 2000: Reminder and complex order.
 20th April, 2000: index an invertibility.
 24th April, 2000: Fredholm determinant and 1form.
 25th April, 2000: 2form and invertibility of families.
 27th April, 2000: Determinant bundle and curvature.

Lecture Notes
Revised versions of the lecture notes will be provided as I go along.
 Tempered distributions and the Fourier transform,
Last revision 3rd February, 2000:
Chapter1.ps
(Postscript):
Chapter1.dvi
(Dvi)
 Pseudodifferential operators on Euclidean space,
Last revision 6th March, 2000 (from 3rd February, 2000)  small changes and sections moved into Chapter 3:
Chapter2.ps
(Postscript)
Chapter2.dvi
(Dvi)
 Isotropic and scattering calculi,
Last revision (Fredholm determinant and alternative sections added) 10 May, 2000:
Chapter3.ps
(Postscript)
Chapter3.dvi
(Dvi)
 Bibliography etc:
Rear.ps
(Postscript)
Rear.dvi
(Dvi)