PH30025: Mathematical methods
[Page last updated: 21 April 2022]
Academic Year:  2022/3 
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 ) OR take PH20107

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.

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.

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: 
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)
 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)
 USPHAFM02 : MPhys(Hons) Physics (Year 3)
 USPHAFM04 : MPhys(Hons) Physics with Research placement (Year 3)
 USPHAAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
 USPHAKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
 USPHAKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
 USPHAFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
 USPHAFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
 USPHAAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
 USPHAKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
 USPHAKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
 USPHAAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 4)
 USPHAAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (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)
 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)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)

Notes:  This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
 Programmes and units are subject to change 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
