Undergraduate Course: Methods of Mathematical Physics (PHYS10034)
|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
|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.
- 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
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2021/22, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Degree Examination, 100%
Visiting Student Variant Assessment
Degree Examination, 100%
||One to one communication during workshops.
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
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.
|Course organiser||Dr Kristel Torokoff
Tel: (0131 6)50 5270
|Course secretary||Miss Denise Fernandes Do Couto
Tel: (0131 6)51 7521