MATH 654 - Advanced Analysis and Applications

Advanced Analysis and Applications - MATH 654

Lecture Meeting: Thursday 1600 - 1900

Catalog Description

Banach and Hilbert spaces, linear operators, Riez representation theorem, Hahn Banach theorem , uniform boundedness theorem, open mapping theorem, inverse mapping theorem, closed graph theorem, dual spaces, introduction to spectral theory, operators on normed spaces, Sobolev spaces and applications to linear differential equations.

Course Objectives

Teach the students the theory of Hilbert spaces, Sobolev spaces and some application in Partial differential Equations and related subjects.

Course Outcomes

1) Knowledge and Understanding: During the lecture the student learns to model different types of problems and select the suitable package and existing programs in these packages to solve the given problems.

2) Intellectual Skills: By the end of the course the student is expected to solve real-life problems reflecting the student ability to identify the suitable computational technique for a specific type of problems.

3) Practical Skills: By the end of the course student will have the ability to compare the computational methods for advantages and disadvantages, choose the suitable computational method among several existing methods and implement the computational methods using existing computational software.

4) Transferable Skills: Within the lectures the student is able to transfer ideas and experience, work effectively as a part of a group and independently.

Download course syllabus as PDF