Spring semester

Unit(s) of Assessment	Weighting Towards Module Mark( %)
Coursework	25
Examination	75
Qualifying Condition(s)

This module introduces students to linear partial differential equations (PDEs), mainly in one and two space dimensions.

MS105 Modelling and Experimental Mathematics
MS109 Vector Calculus
MS203 Ordinary Differential Equations

At 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.

The contents of the lectures 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 equation: Mean-value theorem, maximum principle, Poisson formula.

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

3 contact hours for 10 weeks with 30 hours of lectures and tutorials.

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

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

31 July 2007