# TOPICS IN THEORETICAL PHYSICS - 2017/8

Module code: PHYM039

Module provider

Physics

Module Leader

AL-KHALILI JS Prof (Physics)

Number of Credits

15

ECT Credits

15

Framework

FHEQ Level 7

JACs code

F340

Module cap (Maximum number of students)

N/A

Module Availability

Semester 2

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

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

Examination | END OF SEMESTER EXAMINATION 1.5 HOURS | 70% |

Coursework | COURSEWORK | 30% |

Alternative Assessment

N/A

Prerequisites / Co-requisites

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 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 | |
---|---|

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

Module content

I. Functions of complex variables (15 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 (8 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 (7 hours)

Fourier transforms

The Dirac delta function

Laplace transforms

Solving differential equations with Laplace transforms

Convolutions

Methods of Teaching / Learning

30 hours of lectures + 3 hours of tutorials and open discussions.

The final examination will be of 2h duration, with three questions from four 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:

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.

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.

Reading list

Reading list for TOPICS IN THEORETICAL PHYSICS : http://aspire.surrey.ac.uk/modules/phym039

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 2017/8 academic year.