Undergraduate Course: Methods of Mathematical Physics (PHYS10034)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Course type	Standard	Availability	Available to all students
Credit level (Normal year taken)	SCQF Level 10 (Year 4 Undergraduate)	Credits	10
Home subject area	Undergraduate (School of Physics and Astronomy)	Other subject area	None
Course website	http://www2.ph.ed.ac.uk/~dmarendu/MOMP.html	Taught in Gaelic?	No
Course description	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 (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Complex Variable & Differential Equations (MATH10033)	Co-requisites
Prohibited Combinations		Other requirements	At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.
Additional Costs	None

Information for Visiting Students
Pre-requisites	None
Displayed in Visiting Students Prospectus?	Yes

Course Delivery Information

Delivery period: 2012/13 Semester 1, Available to all students (SV1)						WebCT enabled: No		Quota: None
Location	Activity	Description	Weeks	Monday	Tuesday	Wednesday	Thursday	Friday
King's Buildings	Lecture		1-11	14:00 - 14:50
King's Buildings	Lecture		1-11				14:00 - 14:50
King's Buildings	Tutorial		1-11		14:00 - 15:50
First Class	First class information not currently available
Additional information	Workshop/tutorial sessions, as arranged.
Exam Information
Exam Diet	Paper Name		Hours:Minutes
Main Exam Diet S2 (April/May)			2:00

Delivery period: 2012/13 Semester 1, Part-year visiting students only (VV1)						WebCT enabled: No		Quota: None
Location	Activity	Description	Weeks	Monday	Tuesday	Wednesday	Thursday	Friday
King's Buildings	Lecture		1-11	14:00 - 14:50
King's Buildings	Lecture		1-11				14:00 - 14:50
First Class	First class information not currently available
Additional information	Workshop/tutorial sessions, as arranged.
Exam Information
Exam Diet	Paper Name		Hours:Minutes
Main Exam Diet S1 (December)			2:00

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

Assessment Information
Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%

Special Arrangements
None

Additional Information
Academic description	Not entered
Syllabus	&� Revision of infinite series; asymptotic series &� Complex analysis: revision, residues and analytical continuation &� Gamma function &� Laplace and stationary phase methods; saddle point approximation &� Dirac's delta function &� Ordinary differential equations (ODEs): Green functions and solution via series &� Special functions &� Fourier transformations: definition, properties and application to ODEs &� Laplace transforms: definition, properties and application to ODEs &� Partial differential equations: characterisation and solution via Laplace and Fourier transforms &� Examples: the wave equation, the diffusion equation and Laplace equation
Transferable skills	Not entered
Reading list	Not entered
Study Abroad	Not entered
Study Pattern	Not entered
Keywords	MoMP