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Programme & Unit Catalogues

## MA40059: Mathematical methods 2

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 2
Assessment Summary: CW 20%, EX 80%
Assessment Detail:
• Coursework (CW 20%)
• Examination (EX 80%)
Supplementary Assessment: MA40059 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA40044 and in taking this unit you cannot take MA30059. This unit may only be taken by students on Mathematics and Physics programmes.
Description: Aims & Learning Objectives:
Aims:
To introduce students to the applications of advanced analysis to the solution of PDEs, including examples drawn from topics in advanced physics.
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, and in cases interpret these in physical terms. 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. Self-adjoint second-order operators: Eigenvalue problems (mainly by example). Separation of variables for inhomogeneous systems. Green's function methods in general: Method of images. Use if 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 non-integral constraints. Applications to physical problems: Translate advanced physical problems into mathematical form; obtain and interpret mathematical solutions.
Programme availability:

#### MA40059 is Compulsory on the following programmes:

Department of Physics
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.