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; SturmLiouville 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

Information for Visiting Students
Prerequisites  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.

Contacts
Course organiser  Dr Kristel Torokoff
Tel: (0131 6)50 5270
Email: kristel.torokoff@ed.ac.uk 
Course secretary  Miss Hayley Crawford
Tel: (0131 6)51 7524
Email: hayley.crawford@ed.ac.uk 

