Functional Analysis and the Related Quantum Theory.
This is an introductory course to modern functional analysis and its use in the study of PDE of Mathematical-Physics. Beginning with a review of Hilbert spaces and linear operators, we then proceed to the basics of spectral theory of self adjoint operators in Hilbert space, and applications to Fundamental mathematical aspects of Quantum mechanics, and more general Dispersive wave equations.
The necessary Analysis will be developed in class.
This course is also available by arrangement.
Functional Analysis, by M. Reed and B. Simon
Recommended Text: Functional Analysis, by Yoshida, Kosaku
Operator Theory, part 4, by Barry Simon
Real Analysis and Linear Algebra are prerequisites.