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PHYS3591: MATHEMATICS WORKSHOP

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Physics

Prerequisites

  • Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031).

Corequisites

  • Foundations of Physics 3A (PHYS3621).

Excluded Combinations of Modules

  • None.

Aims

  • This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
  • It builds on the Level 2 module Mathematical Methods in Physics (PHYS2611).
  • It provides the mathematical tools appropriate to Level 3 physics students necessary to tackle a variety of physical problems.

Content

  • The syllabus contains:
  • Vectors and matrices, Hilbert spaces, linear operators, matrices, eigenvalue problem, diagonalisation of matrices, co-ordinate transformations, tensor calculus.
  • Complex Analysis: functions of complex variables, differentiable functions, Cauchy-Riemann conditions, Harmonic functions, multiple valued functions and Riemann surfaces, branch points and cuts, complex integration, Cauchy's theorem, Taylor and Laurent series, poles and residues, residue theorem and definite integrals, residue theorem and series summation.
  • Calculus of Variations: EulerLagrange equations, classic variational problems, Lagrange multipliers.
  • Infinite series and convergence, asymptotic series. Integration, Gaussian and related integrals, gamma function.
  • Integral Transforms: Fourier series and transforms, convolution theorem, Parseval's relation, Wiener-Khinchin theorem. Momentum representation in quantum mechanics, Hilbert transform, sampling theorem, Laplace transform, inverse Laplace transform and Bromwich integral.

Learning Outcomes

Subject-specific Knowledge:

  • Having studied this module students will have knowledge of and an ability to use a range of mathematical methods needed to solve a wide array of physical problems.

Subject-specific Skills:

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Teaching will be by two-hour workshops which are a mix of lectures and examples classes.
  • The lectures provide the means to give a concise, focussed presentation of the subject matter of the module. The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.
  • When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.
  • New material is immediately backed up by example classes which give students the chance to develop their theoretical understanding and problem solving skills.
  • Students will be able to obtain further help in their studies by approaching their lecturers, during the workshop sessions or at other mutually convenient times.
  • Student performance will be summatively assessed through two open-book examinations.
  • The example classes provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Workshops36Twice weekly2 Hours72 
Preparation and Reading128 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
two-hour open-book written examination 1 50 
two-hour open book written examination 2 50 

Formative Assessment

None.

More information

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Current Students: Please contact your department.