Methods of Mathematical Physics (U01413)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : PHY-4-MPMeth

A course on advanced methods of mathematical physics. The course aims to demonstrate the utility and limitations of a variety of powerful calculational techniques and to provide a deeper understanding of the mathematics underpinning theoretical physics. The course will review and develop the theory of: complex analysis and applications to special functions; asymptotic expansions; ordinary and partial differential equations, in particular, characteristics, integral transform and Green function techniques; Dirac delta and generalised functions; Sturm-Liouville theory. The generality of approaches will be emphasised and illustrative examples from electrodynamics, quantum and statistical mechanics will be given.

Entry Requirements

? Pre-requisites : At least 40 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q; Complex Variables & Differential Equations (MAT-3-CVD) from Schedule P, or equivalent.

Variants

? This course has variants for part year visiting students, as follows

Methods of Mathematical Physics (VS1) (Not being delivered)

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
20/09/2007	14:00	15:00	Lecture Room 3218, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	14:00	14:50	KB
Lecture	Thursday	14:00	14:50	KB

? Additional Class Information : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

On completion of this course a student should be able to:
1)define and derive convergent and asymptotic series
2)apply techniques of complex analysis, such as contour integrals and analaytic continuation, to the study of special functions of mathematical physics
3)calculate approximations to integrals by appropriate saddle point methods
4)define and manipulate the Dirac Delta and other distributions and be able to derive their various properties
5)be fluent in the use of Fourier and Laplace transformations to solve differential equations and derive asymptotic properties of solutions
6)solve partial differential equations with appropriate initial or boundary conditions with Green function techniques
7)have confidence in solving mathematical problems arising in physics by a variety of mathematical techniques