PH30025: Mathematical methods
[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: | Honours (FHEQ level 6) |
| Period: |
- Semester 2
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| Assessment Summary: | EX 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 PH20019 AND take PH20020 ) OR take PH20107
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| 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 Euler-Lagrange equation and solve problems using the calculus of variations.
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| 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.
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| Skills: | Numeracy T/F A, Problem Solving T/F A.
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| Content: | Functions of a complex variable (11 hours): 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. Kramers-Kronig relations.
Superposition methods (5 hours): 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.
Calculus of variations (6 hours): Euler-Lagrange equation: derivation and examples. Variation subject to constraints: examples.
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| Course availability: |
PH30025 is Optional on the following courses:
Department of Chemistry
- USSC-AFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
- USSC-AAB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 4)
- USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
- USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
- USSC-AFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
- USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 4)
- USSC-AFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
- USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
- USSC-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
- USSC-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
Department of Physics
- USPH-AFB01 : BSc(Hons) Physics (Year 3)
- USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
- USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
- USPH-AFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
- USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 4)
- USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 4)
- USPH-AFM02 : MPhys(Hons) Physics (Year 3)
- USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
- USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
- USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
- USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
- USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
- USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
- USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
- USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
- USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
- USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 4)
- USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 4)
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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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