Student Records
Programme & Unit Catalogues

## PH30025: Mathematical methods

Academic Year: 2014/5
Owning Department/School: Department of Physics
Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (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 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.
Programme availability:

#### PH30025 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 3)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 4)
Department of Physics
• USPH-AFB01 : BSc(Hons) Physics (Year 3)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
• USPH-AFB09 : BSc Physics (Year 3)
• USPH-AFM02 : MPhys(Hons) Physics (Year 3)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 3)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 4)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.