Course Details in 2025/26 Session

Module Title	LM Complex Variable Theory
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	06 18779
Module Lead	Yulii Shikhmurzaev
Level	Masters Level
Credits	10
Semester	Semester 1
Pre-requisites
Co-requisites
Restrictions	Optional: Undergraduate masters programmes in Physics (excluding TPAM and Physics with Theory). Cannot be taken if 06 06205 has already been taken.
Contact Hours	Lecture-23 hours Tutorial-5 hours Total: 28 hours
Exclusions
Description	This module covers those elements of Complex Variable Theory that form part of the toolbox of a theoretical physicist. This includes analytic functions, Cauchy-Riemann equations, Taylor's Theorem, simple convergence tests, non-analyticity, simple and multiple poles, Laurent series, convergence and simple analytical continuation, residues and their calculation, branch points, cuts and more on analytic continuation, Cauchy's theorem and Cauchy's integral formulae, residue theorem and lots of applications including integrands with cuts.
Learning Outcomes	By the end of the module the student should be able to:Determine whether a complex function is analytic and identify its singular points;Evaluate Taylor and Laurent series of complex valued functions and make elementary checks on their convergence properties;Determine and identify poles of complex valued functions;Apply Cauchy's integral formula and the Residue Theorem to evaluate integrals;Understand and use the concepts of branch points and cuts, particularly in the context of contour integration integrals;Explore this topic beyond the taught syllabus.
Assessment	18779-01 : Exam : Exam (Centrally Timetabled) - Written Unseen (100%)
Assessment Methods & Exceptions	Assessment: 2 hour Examination (100%)
Other
Reading List	Spiegel MR, Theory and Problems of Complex Variables, Schaum's Outline Series, McGraw-Hill Kreyzig E, Advanced Engineering Mathematics, Wiley, 7th Ed Brown JW and Churchill RV, Complex Variables and Applications, McGraw-Hill, 6th Ed Jeffrey A, Advanced Engineering Mathematics, Academic Press - International Edition Arfken GB and Weber HJ, Mathematical Methods for Physicists, Academic Press, 5th Ed Riley KF, Hobson MP and Bence SJ, Mathematical Methods for Physics and Engineering, CUP O'Neil and Wadsworth, Advanced Engineering Mathematics, 3rd Ed