Undergraduate Course: Methods of Mathematical Physics (PHYS10034)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | 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. |
| Course description |
- 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
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2022/23, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 20,
Summative Assessment Hours 2,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
50 )
|
| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Degree Examination, 100%
Visiting Student Variant Assessment
Degree Examination, 100% |
| Feedback |
One to one communication during workshops.
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Apply techniques of complex analysis, such as contour integrals and analaytic continuation, to the study of special functions of mathematical physics .
- Calculate approximations to integrals by appropriate saddle point methods.
- Be fluent in the use of Fourier and Laplace transformations to solve differential equations and derive asymptotic properties of solutions.
- Solve partial differential equations with appropriate initial or boundary conditions with Green function techniques.
- Have confidence in solving mathematical problems arising in physics by a variety of mathematical techniques.
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Contacts
| Course organiser | Dr Kristel Torokoff
Tel: (0131 6)50 5270
Email: |
Course secretary | Mrs Ola Soldan-Kieliszek
Tel: (0131 6)51 3448
Email: |
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