PH30025: Mathematical methods
[Page last updated: 15 October 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must ( take PH20019 AND take PH20020 ) OR take PH20107 
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 ordinary differential equations; * solve ordinary differential equations using Green functions; * 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 (11 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 (5 hours): SturmLiouville theory, eigenfunctions and eigenvalues, orthogonality of eigenfunctions. Solution of inhomogeneous equations. Green's functions: eigenfunction expansion; direct method; application to solution of inhomogeneous ordinary differential equations. Calculus of variations (6 hours): EulerLagrange equation: derivation and examples. Variation subject to constraints: examples. 
Programme availability: 
PH30025 is Optional on the following programmes:Department of Physics

Notes:
