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 |
https://www.learn.ed.ac.uk/webapps/portal/frameset.jsp |
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: 2013/14 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 |
16/09/2013 |
| 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 )
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| 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
| 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 |
Contacts
| Course organiser | Dr Jennifer Smillie
Tel: (0131 6)50 5239
Email: J.M.Smillie@ed.ac.uk |
Course secretary | Miss Paula Wilkie
Tel: (0131) 668 8403
Email: Paula.Wilkie@ed.ac.uk |
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