杏吧论坛

Dr Robert Simon

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.

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.

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.

20 hours of lectures and 10 hours of seminars in the MT. 2 hours of lectures in the ST.

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.

Exam (90%, duration: 2 hours) in the summer exam period.
Coursework (10%) in the LT.