MA26510 Methods of Mathematical Modelling 3
Introductory description
Our comprehension of many phenomena in the world relies heavily on partial differential equations (PDEs). These equations are instrumental to describe various phenomena such as heat propagation, the vibrations of solids, fluid dynamics, chemical reactions, photonelectron interactions, or electromagnetic wave radiation. Moreover, PDEs play an important role in contemporary mathematics, particularly in geometry and analysis.
This course will give an introduction providing insights into mathematical modeling, the fundamental properties of partial differential equations and the methodologies employed in their analysis.
Module aims
The module aims at providing a broad perspective on the subject, and illustrate the rich variety of phenomena which can be described by PDEs. It will provide students with the most important techniques to construct socalled classic solutions to PDEs – the methods of characteristics, the method of the separation of variables as well as Fourier series. Students will learn to differentiate cetrain types of PDEs and comprehend their inherent characteristics. The modeule will also illustrate how PDEs arise naturally in the phyiscal and life sciences.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
The course will start with an introduction to PDES, outlining what PDEs actually are, how some of them can be classified, how do they arise in physics and the life sciences, and what the notion of wellposedness means. It will mainly focus on three classical equations – the heat equation, the wave equation and the Laplace equation – on unbounded and bounded domains.
Learning outcomes
By the end of the module, students should be able to:
 understand and apply fundamental physical principles to derive certain types of PDEs.
 the ability to differentiate between various types of PDEs and comprehend the distinctions in their inherent characteristics.
 calculate solutions to the three main types of PDEs on unbounded and bounded domains
 You will also understand that properties of solutions to PDEs sensitively depend on the type.
Indicative reading list
W. Strauss Partial Differential Equations, an introduction Wiley 1992
J.D. Logan Applied Partial Differential Equations, 2nd edition Springer, 2004
Subject specific skills
At the end, students will be familiar with the notion of wellposed PDE problems and have an idea what kind of initial or boundary conditions may be imposed for this purpose. Students will have studied some techniques which enable you to solve some simple PDE problems. They will also understand that properties of solutions to PDEs sensitively depend on the type.
Transferable skills
The module provides technical competence in solving basic partial differential equations that feature at least as building blocks in applications. There are aspects of critical thinking and creativity related to analysing and solving PDE problems.
Study time
Type  Required 

Lectures  30 sessions of 1 hour (30%) 
Seminars  9 sessions of 1 hour (9%) 
Private study  61 hours (61%) 
Total  100 hours 
Private study description
Working on assignments, going over lecture notes, text books, exam revision.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Assignments  15%  
Examination  85% 
Assessment group R1
Weighting  Study time  

Inperson Examination  Resit  100% 
Feedback on assessment
Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.
Courses
This module is Core for:
 Year 2 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)

UMAAG100 Undergraduate Mathematics (BSc)
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 2 of G100 Mathematics
 Year 2 of G103 Mathematics (MMath)
 Year 2 of G103 Mathematics (MMath)
 Year 2 of UMAAG107 Undergraduate Mathematics (MMath) with Study Abroad
 Year 2 of UMAAG101 Undergraduate Mathematics with Intercalated Year