## MAMCDTE-Partial Differential Equations

Module Provider: Mathematics and Statistics
Number of credits: 12 [6 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites: MAMCDTS Dynamical Systems and MAMCDTU Data & Uncertainty and MAMCDTN Numerical Methods
Modules excluded:
Module version for: 2017/8

Module Convenor: Dr Tristan Pryer

Summary module description:
Note: As this module is part of a joint programme with Imperial College London, the academic regulations for this module might differ from standard academic regulations usually applied at the University of Reading. The relevant document is the Joint Degree Programme Agreement between Imperial College London and University of Reading.

Aims:

The aims of this module are:

1) To give an overview of the modern theory of PDEs, using the example of the fundamental equations of geophysical fluid dynamics to present the most effective tools at our disposal for obtaining qualitative and quantitative information;

2) To review tools in functional analysis as applied to the study of specific 1- and 2-D PDEs;

3) To provide an overview of variational formulations of geophysical fluid dynamics 4) To provide context in climate and weather.

Assessable learning outcomes:

• Understand the concept of solution of a linear/nonlinear PDEs;

• Use weak and strong formulations of PDEs;

• Understand conservative/dissipative geophysical fluid models;

• Derive numerical schemes for linear PDEs in 1 dimension, and analyse their stability, consistency and convergence;

• Prove stability and calculate dispersion and diffusion error using von Neumann analysis.

Outline content:
Introduction to PDE using the fundamental example of Navier-Stokes(NS)/Euler equations. Discuss the terms in the equations, their physical and mathematical meaning. Then consider one-dimensional examples (Stokes, Burgers, Boussinesq equations) to discuss theoretical foundations such as weak and strong solutions, Fourier methods, variational formulations and conservation laws for geophysical fluid models, arriving to an overview of 2D reduction of NS.

Brief description of teaching and learning methods:
Lectures and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 6 Guided independent study 94 Total hours by term 120.00 Total hours for module 120.00

Summative Assessment Methods:
 Method Percentage Set exercise 50 Class test administered by School 50

Other information on summative assessment:
Where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment methods:

Peer marked tutorial questions.

Penalties for late submission:

Where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Penalties for late submission on this module are in accordance with the University policy. Please refer to page 5 of the Postgraduate Guide to Assessment for further information: http://www.reading.ac.uk/internal/exams/student/exa-guidePG.aspx

Length of examination:

Requirements for a pass:
An average of 50% across the whole module.

Reassessment arrangements:
Via a written resit exam. Coursework will be carried forward if it received 40% or more, otherwise it must be resubmitted before the resit exam.