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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
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA 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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Complex Variables (MATH10067) OR Methods of Theoretical Physics (PHYS10105)
Prohibited Combinations Other requirements At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  0
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
Resit Exam Diet (August)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Apply techniques of complex analysis, such as contour integrals and analaytic continuation, to the study of special functions of mathematical physics .
  2. Calculate approximations to integrals by appropriate saddle point methods.
  3. Be fluent in the use of Fourier and Laplace transformations to solve differential equations and derive asymptotic properties of solutions.
  4. Solve partial differential equations with appropriate initial or boundary conditions with Green function techniques.
  5. Have confidence in solving mathematical problems arising in physics by a variety of mathematical techniques.
Reading List
Additional Information
Course URL
Graduate Attributes and Skills Not entered
Additional Class Delivery Information Workshop/tutorial sessions, as arranged.
Course organiserDr Kristel Torokoff
Tel: (0131 6)50 5270
Course secretaryMs Dipti Dineshwar
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