Not available in 2022/23
MA412 Half Unit
Functional Analysis and its Applications
This information is for the 2022/23 session.
Teacher responsible
Dr Robert Simon
Availability
This course is available on the MSc in Applicable Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.
Pre-requisites
Students should have taken a course in finite dimensional linear algebra which includes diagonisation and inner products. General knowledge of real analysis and calculus would be helpful.
Course content
This course aims at familiarizing the student with the basic concepts, principles and methods of functional analysis and its applications. The topics covered are: normed and Banach spaces, continuous linear transformations, inner product and Hilbert spaces, compact operators, Hahn-Banach and Baire Category Theorems, applications to differential equations, numerical analysis, and approximation theory with illustrative examples.
Teaching
20 hours of lectures and 10 hours of seminars in the MT. 2 hours of lectures in the ST.
Indicative reading
Jean-Pierre Aubin, Applied Functional Analysis, Wiley, 2000; A.V. Balakrishnan, Applied Functional Analysis, Springer, 1981; Erwin Kreyszig, Introductory Functional Analysis with Applications, John Wiley, 1989; David Luenberger, Optimization by Vector Space Methods, Wiley-Interscience, 1997; Walter Rudin, Functional Analysis, McGraw-Hill 1991; Nicholas Young, An Introduction to Hilbert Space, Cambridge University Press, 1988.
Assessment
Exam (90%, duration: 2 hours) in the summer exam period.
Coursework (10%) in the LT.
Key facts
Department: Mathematics
Total students 2021/22: Unavailable
Average class size 2021/22: Unavailable
Controlled access 2021/22: No
Value: Half Unit
Course selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills