 
Summary: AMAT 487 and 587: Topics in Modern Mathematics
SUNY Albany, Spring 2011
Tu Th 11:45 am  1:05 pm in ES 146
Instructor: Ivana Alexandrova
Course Description
In this course we will discuss the fundamentals of linear partial differential equations.
We will begin with an introduction to the theory of distributions. We will then discuss
how the motivation for semiclassical analysis arises from quantum mechanics. After that
we will introduce the classes of semiclassical symbols and will study their quantizations to
pseudodifferential operators. We will further introduce canonical relations and study their
quantizations to Fourier integral operators. We will also discuss applications of this theory
to the analysis of linear partial differential equations. The course grade will be based on
homework sets.
Prerequisites: A completed undergraduate course on real analysis. Some knowledge of func
tional analysis is a plus.
Required textbooks:
An Introduction to the Theory of Distributions, F.G. Friedlander and Mark Joshi
An Introduction to Semiclassical and Microlocal Analysis, AndrŽe Martinez
Other references:
The Analysis of Linear Partial Differential Operators, Vol. I, Lars Hšormander
