| Instructor | Orlando Merino, merino@math.uri.edu, 874-4442, Tyler Hall 220 |
| Meets |
TuTh 2-3:15 p.m. at the conference room of the Mathematics Department. Send email to merino@math.uri.edu to receive updates on mth629's schedule. |
| 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) |