
Academic Year:  2012/3 
Owning Department/School:  Department of Physics 
Credits:  6 
Level:  Honours (FHEQ level 6) 
Period: 
Semester 2 
Assessment:  EX 100% 
Supplementary Assessment:  Mandatory extra work (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take PH20019 and take PH20020 
Description:  Aims: The aim of this unit is to continue the development of students' mathematical knowledge and skills by introducing concepts and methods used in a mathematical description of the physical world. Learning Outcomes: After taking this unit the student should be able to: * derive theorems of analytic functions and use them to evaluate integrals; * use superposition methods for inhomogeneous equations; * solve problems in scattering theory; * derive the EulerLagrange equation and solve problems using the calculus of variations. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Functions of a complex variable (10 hours): Functions of z, multivalued functions, branch points and branch cuts. Differentiation, analytic functions, CauchyRiemann equations. Complex integration; Cauchy's theorem and integral. Taylor and Laurent expansions. Residue theorem, evaluation of real integrals. KramersKronig relations. Superposition methods (8 hours): SturmLiouville theory, eigenfunctions and eigenvalues, orthogonality of eigenfunctions. Solution of inhomogeneous equations. Green's functions. Examples using 1D and 3D operators. Scattering theory. Calculus of variations (4 hours): EulerLagrange equation: derivation and examples. Inclusion of constraints: Lagrange multipliers, examples. 
Programme availability: 
PH30025 is Optional on the following programmes:Programmes in Natural Sciences
