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2010/1 Module Catalogue
 Module Code: MAT2011 Module Title: LINEAR PDES
Module Provider: Mathematics Short Name: MS217
Level: HE2 Module Co-ordinator: BEVAN JJ Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern
Unit(s) of Assessment
Weighting Towards Module Mark( %)
Class Test
Qualifying Condition(s) 
A weighted aggregate mark of 40% is required to pass this module.
Module Overview
The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions.

MAT1015 Calculus (MS114) 


MAT1016 Linear Algebra (MS124)
MAT1017 Proof, Probabily and Experiment (MS125): Experiment submodule
Module Aims
The aim of this module is to study both qualitative and quantitative aspects of linear PDEs in one and two space dimensions.
Learning Outcomes

By the end of the module, a student should be able to




- classify linear PDEs and choose the appropriate method to solve them;




- solve linear PDEs using the method of characteristics, Fourier transform, and separation of variables;




- interpret solutions;




- understand the use of the maximum principle and energy methods for uniqueness and well-posedness.
Module Content

The contents of the module will include:




- Linear PDEs: Examples, classification of PDEs, their physical interpretation and derivation. 




- First-order PDEs: Method of characteristics.




- Wave and heat equation in one space dimension: d’Alembert’s solution, energy methods, Fourier series, Fourier transform, and solution of boundary-value problems through separation of variables.




- Interpretation of solutions.




- Laplace ’s equation: mean-value theorem, maximum principle, Poisson formula.
Methods of Teaching/Learning

Teaching is by lectures, tutorials and example classes. Learning takes place through lectures, exercises (example sheets), preparation for tests and background reading.




There will be 3 contact hours for 10 weeks consisting of lectures, tutorials and example classes.
Selected Texts/Journals

- P.V. O'Neil, Beginning Partial Differential Equations, John Wiley & Sons, (1999).




- W.A. Strauss, Partial Differential Equations, John Wiley & Sons, (1992).


Last Updated
September 10