## MA412Half UnitFunctional Analysis and its Applications

This information is for the 2016/17 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, applications to differential equations, numerical analysis, optimization, and approximation theory with illustrative examples.

Teaching

20 hours of lectures and 10 hours of seminars in the MT. 1 hour of seminars 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.

Assessment

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

Key facts

Department: Mathematics

Total students 2015/16: 6

Average class size 2015/16: 6

Controlled access 2015/16: 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

Course survey results

(2012/13 - 2014/15 combined)

1 = "best" score, 5 = "worst" score

The scores below are average responses.

Response rate: 67%

Question

Average
response

2.2

Materials (Q2.3)

2.1

Course satisfied (Q2.4)

2.2

Lectures (Q2.5)

2.2

Integration (Q2.6)

1.9

Contact (Q2.7)

2.2

Feedback (Q2.8)

2.4

Recommend (Q2.9)

 Yes 65% Maybe 6% No 29%