
Module Availability 
Spring 


Assessment Pattern 
Unit(s) of Assessment

Weighting Towards Module Mark( %)

Assignment

15

Class Test

10

Examination

75

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. 


Prerequisites/Corequisites 
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 wellposedness. 


Module Content 
The contents of the module will include:
 Linear PDEs: Examples, classification of PDEs, their physical interpretation and derivation.
 Firstorder 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 boundaryvalue problems through separation of variables.
 Interpretation of solutions.

Laplace
’s equation: meanvalue 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 
