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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Methods of Mathematical Physics (PHYS10034)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) Credits10
Home subject areaUndergraduate (School of Physics and Astronomy) Other subject areaNone
Course website Taught in Gaelic?No
Course descriptionA 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)
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
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2014/15 Semester 1, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Class Delivery Information Workshop/tutorial sessions, as arranged.
Course Start Date 15/09/2014
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 2, Revision Session Hours 4, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 60 )
Additional Notes
Breakdown of Assessment Methods (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
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
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
Course organiserDr Kristel Torokoff
Tel: (0131 6)50 5270
Course secretaryMiss Paula Wilkie
Tel: (0131) 668 8403
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