# TOPICS IN THEORETICAL PHYSICS - 2021/2

Module code: PHYM039

## Module Overview

This 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.

### Module provider

Mathematics & Physics

### Module Leader

ROCCO Andrea (Biosc & Med)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 7

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 106

Tutorial Hours: 11

Guided Learning: 11

Captured Content: 22

## Module Availability

Semester 2

## Prerequisites / Co-requisites

None

## Module content

**I. Functions of complex variables (12 hours)**

- Continuity and differentiability
- The Cauchy-Riemann conditions
- Analyticity, singularities, poles.
- Complex integration
- Cauchy's theorem
- Residues and the residue theorem
- Taylor and Laurent series
- Laplace's equation in 2D and conformal mapping
- Laplace and Fourier transforms
- Dispersion relations

**II. Calculus of Variations (9 hours)**

- Integral principles in physics
- Principle of least action and other minimisation problems
- Lagrangian mechanics
- Euler-Lagrange equations
- Applications in configuration space
- Variation subject to constraints
- Extension to functions of more than one variable
- Isoperimetric problems and Lagrange multipliers

**III. Integral Transforms (5 hours)**

- Fourier transforms
- The Dirac delta function
- Laplace transforms
- Solving differential equations with Laplace transforms
- Convolutions

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Coursework | COURSEWORK | 100 |

## Alternative Assessment

N/A

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate

This module introduces students to a range of mathematical techniques of use across theoretical physics. The end of semester examination is test and allows the students to demonstrate their understanding of mathematical techniques, their derivation (bookwork), their applications in physical examples, both of a type they have encountered in lectures and in the process of solving the examples in problem sheets and more original problems not encountered.

Thus, the __summative assessment__ for this module consists of:

This module is assessed entirely by an end of semester examination, two hours long, in which the student must answer 3 from 4 questions covering all areas of the course.

__Formative assessment and feedback__

Regular feedback on previously taught material at the beginning of a lecture and discussion of problems and issues encountered in working through the problem sheets. Students will submit their solutions to selected problems from the sheets set for formative assessment ahead of the tutorial session. These submissions will be marked and feedback given to the students during the tutorial sessions. Model solutions to all problem sheet questions are made available after the students have had sufficient time to tackle them themselves. A revision class is set at the end of the module to go through past examination papers.

## Module aims

- To provide a sound grounding two important topics mathematical physics: Complex Variable Theory and Calculus of Variations. In particular, the basic theorems, methods and applications of functions of a complex variable, a range of advanced integration techniques and theorems and their applications in a range of physical examples and variational principles in classical mechanics leading to both Lagrangian and Hamiltonian formulations.

## Learning outcomes

Attributes Developed | ||

1 | On successful completion of this module, students will have a solid understanding of complex variable theory. They will be able to test a function for analyticity and identify and classify poles and other singular points of functions. Students will be familiar with methods for performing real and complex variable integrals by complex contour integration using techniques such as the Residue theorem. They will have a solid grounding in both Lagrangian and Hamiltonian mechanics and in the methods of calculus of variations and be able to assess how these can be applied across a wide range of physics problems, and be able to calculate solutions to such problems. |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

26 hours of lectures + 7 hours of tutorials and open discussions (33 contact hours in total).

In addition there is expected to be open-ended study to work on tutorial problem and the assessed coursework.

The final examination will be of 1.5h duration, with two questions from three to be answered.

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate:

This module introduces students to a range of mathematical techniques of use across theoretical physics. The end of semester examination is test and allows the students to demonstrate their understanding of mathematical techniques, their derivation (bookwork), their applications in physical examples, both of a type they have encountered in lectures and in the process of solving the examples in problem sheets and more original problems not encountered.

Thus, the __summative assessment__ for this module consists of:

Coursework to be completed during the semester. It will be made available during week 7 with a submission deadline in week 12.

One exam at the end of the semester lasting 1.5 hours (with 2 questions to be answered out of 3).

__Formative assessment and feedback__

Regular feedback on previously taught material at the beginning of a lecture and discussion of problems and issues encountered in working through the problem sheets. Students will submit their solutions to selected problems from the sheets set for formative assessment ahead of the tutorial session. These submissions will be marked and feedback given to the students during the tutorial sessions. Model solutions to all problem sheet questions are made available after the students have had sufficient time to tackle them themselves. A revision class is set at the end of the module to go through past examination papers.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **PHYM039**

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics and Physics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Mathematics and Physics MMath | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Nuclear Astrophysics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Astronomy MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics MSc | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Quantum Technologies MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2021/2 academic year.