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Programme & Unit Catalogues

## MA50059: Mathematical methods 2

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: CW 25%, EX-TH 75%*
Assessment Detail:
• Coursework* (CW 25%)
• Open Book Examination with a Duration of 24 hours* (EX-TH 75%)

*Assessment updated due to Covid-19 disruptions
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
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. They should be able to demonstrate an in-depth understanding of the subject.

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 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 non-integral constraints.
Programme availability:

#### MA50059 is Optional on the following programmes:

Department of Mathematical Sciences

 Notes: This unit catalogue is applicable for the 2019/20 academic year only. Students continuing their studies into 2020/21 and beyond should not assume that this unit will be available in future years in the format displayed here for 2019/20. Programmes and units are subject to change 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.