|
 Academic Year: | 2018/9 | |
| 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 Euler-Lagrange 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, Cauchy-Riemann equations. Complex integration; Cauchy's theorem and integral. Taylor and Laurent expansions. Residue theorem, evaluation of real integrals. Kramers-Kronig relations. Superposition methods (5 hours): Sturm-Liouville 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): Euler-Lagrange equation: derivation and examples. Variation subject to constraints: examples. | Before taking this module you must take PH20019 AND take PH20020 |
| Programme availability: |
PH30025 is Compulsory on the following programmes:Programmes in Natural Sciences
PH30025 is Optional on the following programmes:Department of Physics
|
Notes:
|