Not available in 2020/21
MA412      Half Unit
Functional Analysis and its Applications

This information is for the 2020/21 session.

Teacher responsible

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.

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.


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.


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

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: Unavailable

Average class size 2019/20: Unavailable

Controlled access 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills