Academic Year:  2017/8 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 
 Semester 2

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module 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 Compulsory on the following programmes:
Programmes in Natural Sciences
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
PH30025 is Optional on the following programmes:
Department of Physics
 USPHAFB01 : BSc(Hons) Physics (Year 3)
 USPHAAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
 USPHAKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
 USPHAFM02 : MPhys(Hons) Physics (Year 3)
 USPHAFM04 : MPhys(Hons) Physics with Research placement (Year 3)
 USPHAKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
 USPHAKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
 USPHAFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
 USPHAFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
 USPHAFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
 USPHAKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
Programmes in Natural Sciences
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Professional Placement (Year 4)
 UXXXAFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
 UXXXAAB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
 UXXXAKB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
