MTH5123 · Partial differential equations

Overview

Partial Differential Equations are ubiquitous in the modelling of physical phenomena. This topic will introduce the modern theory of partial differential equations of different types, in particular the existence of solutions in an appropriate space. Fourier analysis, one of the most powerful tools of modern analysis, will also be covered. The following topics are covered in the unit: Sobolev spaces theory (weak derivatives, continuous and compact embeddings, trace theorem); elliptic equations (weak solutions, Lax-Milgram theorem); Parabolic equation (existence, maximal principle); Hyperbolic and dispersive equations (well-posedness).

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Synthetise advanced mathematical knowledge in the basic theory of fundamental PDEs.
2. Interpret the construction of `generalised functions' (distribution) and how it relates to modern notions of derivative and function spaces.
3. Synthetise techniques and properties of Fourier Analysis.
4. Apply sophisticated Fourier analysis methods to problems in PDEs and related fields.
5. Apply recent developments in research on PDEs

Workload

• 3 hours of seminars; • 1 hour applied session and • 10 hours of independent study per week

Student experience, not official rules. Nothing here changes what the Handbook says.