MODULE TITLE

Methods of Theoretical Physics

 

CREDIT VALUE

15

MODULE CODE

PHY3062

MODULE CONVENER

Prof. M.E. Portnoi

 

 

DURATION

TERM

1

2

3

Number Students Taking Module (anticipated)

46

WEEKS

T1:01-11

 

DESCRIPTION – summary of the module content (100 words)

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 – intentions of the module

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) (see assessment section below for how ILOs will be assessed)

 On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

  1. find a Laurent expansion of a function of a complex variable; identify poles and branch points;
  2. evaluate a wide variety of definite integrals using the calculus of residues;
  3. use symmetry arguments when evaluating integrals;
  4. approximate the value of a definite integral using the method of steepest descent;
  5. deduce the first term in Stirling's expansion of the factorial function;
  6. approximate the value of the ground-state energy of a bound particle by using the variational method;
  7. find approximate solutions of the Shrödinger equation using the WKB method;
  8. identify the point group of a simple symmetric object;
  9. identify the 'bond', 'site' and continuum problems of percolation theory;
  10. solve problems using the theory of conformal mapping;

Discipline Specific Skills and Knowledge:

  1. apply analytical and numerical skills in mathematics;
  2. formulate problems in a logical manner;
  3. adapt and apply the methods discussed in lectures to unseen problems;

Personal and Key Transferable / Employment Skills and Knowledge:

  1. present and justify use of techniques and methods;
  2. work in groups - students are encouraged to work co-operatively together to solve assigned problems.

SYLLABUS PLAN – summary of the structure and academic content of the module

  1. Functions of a Complex Variable
    1. Revision of basic notations and properties of complex numbers
    2. Analytic functions
    3. Cauchy's theorem
    4. Laurent expansion
    5. Calculus of residues
  2. Evaluation of Integrals
    1. Elementary methods
    2. Use of symmetry
    3. Contour integration
  3. Conformal Mapping
    1. Theory
    2. Applications
  4. Approximate Methods
    1. Method of steepest descent
    2. The WKB method
    3. Variational method in quantum mechanics
  5. Special Chapters
    1. Elements of group theory
    2. Elements of percolation theory
    3. Non-linear Shrödinger equation (an example)

 

LEARNING AND TEACHING

 

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching activities  

22 hours

Guided independent study  

128 hours

Placement/study abroad

0 hours

 

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

 Category 

 Hours of study time 

 Description 

Scheduled Learning & Teaching activities

20 hours

20×1-hour lectures

Scheduled Learning & Teaching activities

2 hours

2×1-hour problems/revision classes

Guided independent study

30 hours

5×6-hour self-study packages

Guided independent study

16 hours

4×4-hour problem sets

Guided independent study

82 hours

Reading, private study and revision

 

ASSESSMENT

 

 FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

Form of Assessment

Size of the assessment e.g. duration/length

ILOs assessed

Feedback method

Guided self-study

5×6-hour packages

1-14

Discussion in class

4 × Problems sets

4 hours per set

1-14

Solutions discussed in problems classes.

SUMMATIVE ASSESSMENT (% of credit)

Coursework

0%

Written exams

100%

Practical exams

0%

 

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment

 

% of credit

Size of the assessment e.g. duration/length

 ILOs assessed 

Feedback method

Final Examination

100%

2 hours 30 minutes

1-13

Mark via MyExeter, collective feedback via ELE and solutions.

 DETAILS OF RE-ASSESSMENT (where required by referral or deferral)

Original form of assessment

 Form of re-assessment 

ILOs re-assessed

Time scale for re-assessment

Whole module

Written examination (100%)

1-13

August/September assessment period

RE-ASSESSMENT NOTES  

See Physics Assessment Conventions.

 

RESOURCES

 

 INDICATIVE LEARNING RESOURCES -  The following list is offered as an indication of the type & level of information that you are expected to consult. Further guidance will be provided by the Module Convener.

Core text:

  • Not applicable

Supplementary texts:

ELE:

CREDIT VALUE

15

ECTS VALUE

7.5

PRE-REQUISITE MODULES

Mathematics with Physical Applications (PHY2025)

CO-REQUISITE MODULES

none

NQF LEVEL (FHEQ)

6

AVAILABLE AS DISTANCE LEARNING

NO

ORIGIN DATE

01-Oct-10

LAST REVISION DATE

N/A

KEY WORDS SEARCH

Physics; Method; Integrals; Functions; Theory; Expansion; Laurent; Variational; Calculus; Elements; Variable.

Module Descriptor Template Revised October 2011