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MA40059: Mathematical methods 2

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 20%, EX 80%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 20%)
  • Examination (EX 80%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA40044
In taking this module you cannot take MA30059 . This unit may only be taken by students on Mathematics and Physics programmes.
Further information on descriptions 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.
Further information on programme availabilityProgramme 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)

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