
Academic Year:  2015/6 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Honours (FHEQ level 6) 
Period: 
Semester 2 
Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 
MA30059 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:  Before taking this module you must take MA30044 
Description:  Aims & Learning Objectives: Aims: To introduce students to the applications of advanced analysis to the solution of PDEs. Objectives: Students should be able to obtain solutions to certain important PDEs using a variety of techniques e.g. Green's functions, separation of variables. They should also be familiar with important analytic properties of the solution. Content: Topics will be chosen from the following: Elliptic equations in two independent variables: Harmonic functions. Mean value property. Maximum principle (several proofs). Dirichlet and Neumann problems. Representation of solutions in terms of Green's functions. Continuous dependence of data for Dirichlet problem. Uniqueness. Parabolic equations in two independent variables: Representation theorems. Green's functions. Selfadjoint secondorder operators: Eigenvalue problems (mainly by example). Separation of variables for inhomogeneous systems. Green's function methods in general: Method of images. Use of integral transforms. Conformal mapping. Calculus of variations: Maxima and minima. Lagrange multipliers. Extrema for integral functions. Euler's equation and its special first integrals. Integral and nonintegral constraints. 
Programme availability: 
MA30059 is Optional on the following programmes:Department of Mathematical Sciences
