Instructor  Orlando Merino, merino@math.uri.edu, 8744442, 101C Lippitt Hall 
Meets 
TuTh 23:15 p.m. , Lippitt 201 
Text  Basic Operator Theory, by
I. Gohberg and S. Goldberg, Birkhauser (Springer). ISBN: 0817642625,
or Basic Classes of Linear Operators
By Gohberg Goldberg and Kashooek ISBN10: 3764369302  ISBN13: 9783764369309

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 HahnBanach 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  Introduction to Hilbert Space, by N. Young. Cambridge University Press, 1988. ISBN 0 521 33071 8 