Module Overview

Applied Functional Analysis II

This module continues the development of rigorous integration theory and provides an elementary introduction to Hilbert spaces. It provides a sound foundation in analysis for students wishing to continue their mathematical studies at graduate level.

Module Code

MATH 4816

ECTS Credits


*Curricular information is subject to change

Hilbert spaces. Inner products, the Cauchy-Schwartz inequality, orthogonality. Fourier series with respect to an orthonormal basis, applications to solving differential equations. Parseval's theorem and its application to the Fourier transform. 


Orthogonal complements and projections; best approximations and its applications in numerical analysis. Riesz's representation theorem, braket notation.


Bounded linear operators on a Hilbert space. Introduction to Spectral theory: eigenvalues and eigenvectors, spectrum, spectral radius. Neumann series, the spectral radius as a "measure" of an operator, applications to convergence of iterative algorithms. Mathematical formulation of quantum mechanics.

Module Content & Assessment
Assessment Breakdown %
Formal Examination100