2006 Fall MATH 242-01
Bulletin Course Description Metric spaces, fixed point theorems, Baire category theorem, Banach spaces, fundamental theorems of functional analysis, Fourier transform. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title FUNCTIONAL ANALYSIS Department MATH Course Number 2006 Fall 242 Section Number 01 Primary Instructor Beale,James T Permission required? N
Prerequisites
Math 241 or equivalent.
Synopsis of course content
This course is an introduction to functional analysis. In this general approach to analysis, we treat functions as points in vector spaces and work with the properties of these spaces and operators on them. Much of the emphasis is on linear operators as generalizations of what we know from linear algebra in finite dimensions, including the spectrum of such an operator. These ideas were fundamental in the development of quantum mechanics. Notions of convergence and topologies are important in infinite dimensions. This subject is fundamental background for most rigorous analysis, especially in partial differential equations. Topics include Hilbert spaces, Banach spaces, bounded and unbounded operators, compact operators and their spectra, the spectral theorem, and connections with differential equations.
Textbooks
Not yet decided, but we have often used the book by Reed and Simon, Functional Analysis. We will cover most of the content of Chapters 1 through 8 in that book; see the book to get some idea of the material.
Assignments
There will be regular homework assignments.
Grade to be based on
Written work.
