PH20124: Techniques for theoretical physics
[Page last updated: 23 October 2023]
| Academic Year: | 2023/24 |
| Owning Department/School: | Department of Physics |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
- Semester 2
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| Assessment Summary: | EXOB 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take PH20107
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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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| Aims: | The aim of this unit is to further the development of students' mathematical knowledge and skills by introducing concepts and methods used in a mathematical description of the physical world.
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| Skills: | Numeracy T/F A, Problem Solving T/F A.
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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: |
PH20124 is Compulsory on the following courses:
Department of Physics
- USPH-AFB16 : BSc(Hons) Physics with Theoretical Physics (Year 2)
- USPH-AAB16 : BSc(Hons) Physics with Theoretical Physics with Study year abroad (Year 2)
- USPH-AKB16 : BSc(Hons) Physics with Theoretical Physics with Year long work placement (Year 2)
- USPH-AFM16 : MPhys(Hons) Physics with Theoretical Physics (Year 2)
- USPH-AFM17 : MPhys(Hons) Physics with Theoretical Physics with Research placement (Year 2)
- USPH-AAM16 : MPhys(Hons) Physics with Theoretical Physics with Study year abroad (Year 2)
- USPH-AKM16 : MPhys(Hons) Physics with Theoretical Physics with Professional Placement (Year 2)
- USPH-AKM17 : MPhys(Hons) Physics with Theoretical Physics with Professional and Research Placements (Year 2)
- USPH-AAM17 : MPhys(Hons) Physics with Theoretical Physics with Study year abroad and Research Placement (Year 2)
PH20124 is Optional on the following courses:
Department of Physics
- USPH-AFB01 : BSc(Hons) Physics (Year 2)
- USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 2)
- USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 2)
- USPH-AFB10 : BSc(Hons) Physics with Astrophysics (Year 2)
- USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 2)
- USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 2)
- USPH-AFM02 : MPhys(Hons) Physics (Year 2)
- USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 2)
- USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 2)
- USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 2)
- USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 2)
- USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 2)
- USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 2)
- USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 2)
- USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 2)
- USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 2)
- USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 2)
- USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 2)
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Notes: - This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
- 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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