We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Physics

PHYS3591 Mathematics Workshop (2012/13)

Details of the module's prerequisites, learning outcomes, assessment and contact hours are given in the official module description in the Faculty Handbook - follow the link above.  A detailed description of the module's content is given below, together with book lists and a link to the current library catalogue entries.  For an explanation of the library's categorisation system see


Infinite Dimensional Vector Spaces

Dr M. Spannowsky 

9 two-hour workshops in Michaelmas Term

Syllabus: Vector Spaces and Hilbert spaces; Linear operators; Matrices; Eigenvalue Problems; Diagonalisation of Matrices; Co-ordinate Transformations; Tensor Calculus.

Complex Analysis

Dr C. Zambon

9 two-hour workshops in Michaelmas Term

Syllabus: Analytic functions: functions of complex variable; functions differentiable in the complex sense; Cauchy-Riemann conditions; singularities; multiple-valued functions; complex integration and Cauchy's theorem; Taylor and Laurent series; poles and residues; residue theorem and definite integrals; residue theorem and series summation.

Calculus of Variations and Infinite Series

Dr C.J. Maxwell

9 two-hour workshops in Epiphany Term

Syllabus: Calculus of Variations: Euler-Lagrange equations; Classic variational problems: Brachystochrone; Lagrange Multipliers; Isoperimetric problem. Infinite Series: Convergence criteria; Familiar series; Transformation of series; Taylor series for analytic functions; Asymptotic series. Evaluation of Integrals: Change of variables, Gaussian and related integrals, Gamma Function, miscellaneous methods and tricks.

Integral Transforms

Prof S.J. Clark

9 two-hour workshops in Epiphany Term


Additional: Mathematical Methods of Physics, J. Matthews and R.L. Walker (Wiley)
Additional: Mathematical Methods for Physicists, G.B. Arfken and H.J. Weber (Harcourt)
Additional: Mathematical Methods for Physics and Engineering, K.F. Riley, M. P. Hobson and S.J. Bence (Cambridge)

Syllabus: Definition of an integral transform. Fourier transforms; derivation from Fourier series, basic properties and applications, including the convolution theorem, Parseval's relation, and the Wiener-Khinchin theorem. Discrete Fourier transform. Laplace transform; relation to Fourier transform, inverse transform and Bromwich integral, basic properties and applications.

Teaching methods

Workshops: 2 two-hour workshops per week

The format of the workshops will be a combination of lectures and problem-solving classes. The open-book written examinations will be held in the first week of Epiphany and Easter Terms; the exact dates will be announced at the start of the academic year.