Functional Analysis

Undergraduate | 2026

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Area/Catalogue
MATH X305
Course ID icon
Course ID
207619
Level of study
Level of study
Undergraduate
Unit value icon
Unit value
6
Course level icon
Course level
3
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Inbound study abroad and exchange
Inbound study abroad and exchange
The fee you pay will depend on the number and type of courses you study.
Yes
University-wide elective icon
University-wide elective course
Yes
Single course enrollment
Single course enrolment
Yes
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Note:
Course data is interim and subject to change

Course overview

The advances in mathematics and theoretical physics from the start of the twentieth century brought about a need for a more general abstract framework for the study of differential operators, and the functional spaces where these operator act. While Lebesgues theory of integration gave us a precise description of the functions to be studied, it was the development of Hilbert spaces and Banach spaces that gave us the correct setting for the study of operators. In this course we will study Hilbert and Banach spaces, the various notions of convergence on those spaces, and the behaviour of bounded and unbounded operators defined therein. Connections to differential equations will be shown in examples.

  • Normed Linear Spaces

Course learning outcomes

  • Distinguish between different notions of convergence in normed linear spaces;
  • Work with bases on a Hilbert space;
  • Apply the three main theorems (Hahn-Banach, Uniform boundedness, Closed Graph) to a variety of situations
  • Write proofs at an appropriate level
  • Communicate results clearly

Prerequisite(s)

N/A

Corequisite(s)

N/A

Antirequisite(s)

N/A