MTH 629 Spring Semester 2007

Functional Analysis I

Department of Mathematics, U. of Rhode Island


Instructor Orlando Merino,, 874-4442, Tyler Hall 220
Meets TuTh 2-3:15 p.m. at the conference room of the Mathematics Department.
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Text Functional Analysis in Applied Mathematics and Engineering, by M. Pedersen, Chapman & Hall/CRC. ISBN: 0-8493-7169-4.
Prerequisites Linear Algebra, and familiarity with mathematical proofs.
Topics Hilbert and Banach spaces, and continuous linear functions or operators between such spaces. Spectral theory for compact operators is studied in detail, and applications are given to integral and differential equations. Also we will discuss Hahn-Banach theorems and the Banach Contraction Principle and applications.
Evaluation Final Exam (25%), Assignments (75%).
About the Course The course gives an introduction to functional analysis with emphasis on applications. The course is designed for students in mathematics, science, engineering and other fields. Functional Analysis is the study of infinite dimensional vector spaces and functions on these spaces. Functional Analysis provides tools and a foundation for the study of partial differential equations, quantum mechanics, Fourier and wavelet analysis (or harmonic analysis), numerical analysis, approximation theory, and many other fields.
Other texts Basic Operator Theory, by I. Gohberg and S. Goldberg, Birkhauser (Springer). ISBN: 0817642625
Introduction to Hilbert Space, by N. Young. Cambridge University Press, 1988. ISBN 0 521 33071 8
Assignments Homework 1: 1, 2, 3, 6, 9, 12, 13
Homework 2: 14, 21, 22, 23, 30, 31, 36, 37
Homework 3: 40, 42, 48, 49, plus Hahn-Banach thm problems (given later)