MTH5123 - Partial differential equations

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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).

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Zihua Guo

Unit Coordinator(s)

Associate Professor Zihua Guo

Notes

This unit is offered in alternate years commencing Semester 2, 2019

Learning outcomes

On successful completion of this unit, you should be able to:

Synthetise advanced mathematical knowledge in the basic theory of fundamental PDEs.

Interpret the construction of `generalised functions' (distribution) and how it relates to modern notions of derivative and function spaces.

Synthetise techniques and properties of Fourier Analysis.

Apply sophisticated Fourier analysis methods to problems in PDEs and related fields.

Apply recent developments in research on PDEs

Assessment summary

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: If you would otherwise have passed the unit but who do not achieve at least 45% of the marks available for the end-of-semester examination will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. If you are enrolled in MTH5123 you will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4123. The assignments and exam in this unit will use some common items from the MTH4123 assessment tasks, in combination with several higher level questions and tasks.

Workload requirements

Workload

Availability in areas of study

Master of Mathematics