PH22011: Techniques for theoretical physics
[Page last updated: 03 June 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Physics |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
- Semester 2
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| Assessment Summary: | EXOB 100% |
| Assessment Detail: |
- Written examination (EXOB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before or while taking this module you must take PH22006 AND take PH22010
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| Learning Outcomes: |
After taking this unit the student should be able to:
- derive the Euler-Lagrange equation and solve problems using the calculus of variations;
- use superposition methods for inhomogeneous ordinary differential equations;
- solve ordinary differential equations using Green functions;
- derive theorems of analytic functions and use them to evaluate integrals.
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| Synopsis: | This unit is aimed at more theoretically-minded students who want to broaden their mathematical knowledge and skills, both for its own sake and for its application in higher-level theoretical physics units. You will study calculus of variations, Sturm-Liouville theory, Greens functions and functions of a complex variable and see how beautiful mathematical physics can be!
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| Content: | Calculus of variations: Euler-Lagrange equation: derivation and examples. Variation subject to constraints: examples.
Superposition methods: Sturm-Liouville 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.
Functions of a complex variable: 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. Applications to conformal mapping and/or Kramers-Kronig relations.
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| Course availability: |
PH22011 is Compulsory on the following courses:
Department of Physics
- USPH-AFB24 : BSc(Hons) Physics with Theoretical Physics (Year 2)
- USPH-AKB24 : BSc(Hons) Physics with Theoretical Physics with professional placement (Year 2)
- USPH-AKB24 : BSc(Hons) Physics with Theoretical Physics with study abroad (Year 2)
- USPH-AFM24 : MPhys(Hons) Physics with Theoretical Physics (Year 2)
- USPH-AKM24 : MPhys(Hons) Physics with Theoretical Physics with professional placement (Year 2)
- USPH-AFM25 : MPhys(Hons) Physics with Theoretical Physics with research placement (Year 2)
- USPH-AKM25 : MPhys(Hons) Physics with Theoretical Physics with research placement and professional placement (Year 2)
- USPH-AKM25 : MPhys(Hons) Physics with Theoretical Physics with research placement and study abroad (Year 2)
- USPH-AKM24 : MPhys(Hons) Physics with Theoretical Physics with study abroad (Year 2)
PH22011 is Optional on the following courses:
Department of Physics
- USPH-AFB20 : BSc(Hons) Physics (Year 2)
- USPH-AFB22 : BSc(Hons) Physics with Astrophysics (Year 2)
- USPH-AKB22 : BSc(Hons) Physics with Astrophysics with professional placement (Year 2)
- USPH-AKB22 : BSc(Hons) Physics with Astrophysics with study abroad (Year 2)
- USPH-AKB20 : BSc(Hons) Physics with professional placement (Year 2)
- USPH-AKB20 : BSc(Hons) Physics with study abroad (Year 2)
- USPH-AFM20 : MPhys(Hons) Physics (Year 2)
- USPH-AFM22 : MPhys(Hons) Physics with Astrophysics (Year 2)
- USPH-AKM22 : MPhys(Hons) Physics with Astrophysics with professional placement (Year 2)
- USPH-AFM23 : MPhys(Hons) Physics with Astrophysics with research placement (Year 2)
- USPH-AKM23 : MPhys(Hons) Physics with Astrophysics with research placement and professional placement (Year 2)
- USPH-AKM23 : MPhys(Hons) Physics with Astrophysics with research placement and study abroad (Year 2)
- USPH-AKM22 : MPhys(Hons) Physics with Astrophysics with study abroad (Year 2)
- USPH-AKM20 : MPhys(Hons) Physics with professional placement (Year 2)
- USPH-AFM21 : MPhys(Hons) Physics with research placement (Year 2)
- USPH-AKM21 : MPhys(Hons) Physics with research placement and professional placement (Year 2)
- USPH-AKM21 : MPhys(Hons) Physics with research placement and study abroad (Year 2)
- USPH-AKM20 : MPhys(Hons) Physics with study abroad (Year 2)
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Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses 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 pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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