Department of Physics, Unit Catalogue 2010/11 |
PH30025: Mathematical methods |
 Credits:
| 6 |
| Level:
| Honours |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | Like-for-like reassessment (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 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 (10 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 (8 hours): Sturm-Liouville 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): Euler-Lagrange equation: derivation and examples. Inclusion of constraints: Lagrange multipliers, examples. |