MTH4123 - Partial differential equations - 2019

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).

On completion of this unit students will be able to:

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

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam

• 3 hours of lectures and 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics