Functional Analysis- by Reed & Simon part I
Real Analysis, Linear Algebra
Introduction to Math Phys- Quantum mechanics
This is an introductory course to modern analysis in the study of PDE of mathematical-physics. Beginning with 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.