PHY3062 
Methods of Theoretical Physics 
201718 

Dr M.E. Portnoi 


Delivery Weeks: 
T1:0111 

Level: 
6 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
19 students (approx) 

Description
The mathematical techniques presented relate directly to the advanced modules at Stages 3
and 4 of Physics programmes, and also have wide applicability across the mathematical
sciences. Practical skills are emphasised, rather than formal proofs.
Module Aims
This module aims to develop a deeper understanding of, and greater competence in using,
some of the important mathematical methods and techniques of theoretical
physics not covered in PHY2025.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 find a Laurent expansion of a function of a complex variable; identify poles and branch points;
 evaluate a wide variety of definite integrals using the calculus of residues;
 use symmetry arguments when evaluating integrals;
 approximate the value of a definite integral using the method of steepest descent;
 deduce the first term in Stirling's expansion of the factorial function;
 approximate the value of the groundstate energy of a bound particle
by using the variational method;
 find approximate solutions of the Shrödinger equation using the WKB method;
 identify the point group of a simple symmetric object;
 identify the 'bond', 'site' and continuum problems of percolation theory;
 solve problems using the theory of conformal mapping;

Discipline Specific Skills and Knowledge:
 apply analytical and numerical skills in mathematics;
 formulate problems in a logical manner;
 adapt and apply the methods discussed in lectures to unseen problems;

Personal and Key Transferable / Employment Skills and Knowledge:
 present and justify use of techniques and methods;
 work in groups  students are encouraged to work cooperatively together to solve assigned problems.
Syllabus Plan

Functions of a Complex Variable
 Revision of basic notations and properties of complex numbers
 Analytic functions
 Cauchy's theorem
 Laurent expansion
 Calculus of residues

Evaluation of Integrals
 Elementary methods
 Use of symmetry
 Contour integration

Conformal Mapping
 Theory
 Applications

Approximate Methods
 Method of steepest descent
 The WKB method
 Variational method in quantum mechanics

Special Chapters
 Elements of group theory
 Elements of percolation theory
 Nonlinear Shrödinger equation (an example)
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
82 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
114 
Discussion in class 
0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
114 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
113 
Mark via MyExeter, collective feedback via ELE and solutions. 
Resources
The following list is offered as an indication of the type & level of information that
students are expected to consult. Further guidance will be provided by the Module Instructor(s).
Core text:
Supplementary texts:
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Mathematics with Physical Applications (PHY2025) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
113 
August/September assessment period 
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods 
SLT  scheduled learning & teaching activities 
22 hrs 
GIS  guided independent study 
128 hrs 
PLS  placement/study abroad 
0 hrs 
Total 
150 hrs 


Summative assessment 
Coursework 
0% 
Written exams 
100% 
Practical exams 
0% 
Total 
100% 

Miscellaneous
IoP Accreditation Checklist 
 N/A this is an optional module

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Method; Integrals; Functions; Theory; Expansion; Laurent; Variational; Calculus; Elements; Variable. 
Created 
01Oct10 
Revised 
N/A 