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: 
Semester 2

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

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: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020 
PH30025 is Optional on the following programmes:
Department of Physics
 USPHAFB01 : BSc(Hons) Physics (Year 3)
 USPHAFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
 USPHAAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 4)
 USPHAKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 4)
 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)
 USPHAFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
 USPHAKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
 USPHAKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
 USPHAFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
 USPHAKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
 USPHAKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
 USPHAFM04 : MPhys(Hons) Physics with Research placement (Year 3)
 USPHAAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
Programmes in Natural Sciences
 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)
 UXXXAFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
 UXXXAAB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
 UXXXAKB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
 UXXXAFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
 UXXXAAB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
 UXXXAKB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 4)
 UXXXAFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
 UXXXAAB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
 UXXXAKB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
