Programme And Module Handbook
Course Details in 2025/26 Session

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Module Title LH Functional and Fourier Analysis
Department Mathematics
Module Code 06 31129
Module Lead Prof. Jonathan Bennett
Level Honours Level
Credits 20
Semester Semester 2
Pre-requisites LC Vectors, Geometry & Linear Algebra - (06 25664) LI Real & Complex Analysis - (06 25666)
Restrictions None
Contact Hours Lecture-46 hours
Tutorial-10 hours
Guided independent study-144 hours
Total: 200 hours
Description The first half of this module (Functional Analysis) introduces Hilbert spaces, Banach spaces, dual spaces and linear operators, and explores the interaction between linear algebra and analysis in the study of infinite dimensional spaces. The second half (Fourier Analysis) introduces and develops the classical theory of Fourier series and the Fourier transform on the real line, with emphasis on both mathematical rigour and applications.
Learning Outcomes By the end of the module students should be able to:
  • Work in infinite dimensional Hilbert and Banach spaces, find bases for Hilbert spaces, and use several different notions of convergence.
  • Combine ideas from algebra and analysis to solve problems in functional analysis.
  • Understand the basic theory of Fourier series, the Fourier transform, and other related transforms. This will include criteria for the convergence of Fourier series and the invertibility of the Fourier transform.
  • Use Fourier analysis as a tool to understand important classes of partial differential equations, and describe further applications within mathematics.
Assessment 31129-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions "Assessment: 2 hour Summer Examination (80%); In-course Assessment (20%). "
Reading List