Academic Year: |
2014/5 |
Owning Department/School: |
Department of Mathematical Sciences |
Credits: |
6 |
Level: |
Honours (FHEQ level 6) |
Period: |
Semester 2
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Assessment Summary: |
EX 100% |
Assessment Detail: | |
Supplementary Assessment: |
MA30059 Mandatory Extra Work (where allowed by programme regulations)
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Requisites: |
Before taking this unit you must take MA30044 |
Description: |
Aims & Learning Objectives: Aims: To introduce students to the applications of advanced analysis to the solution of PDEs.
Objectives:
Students should be able to obtain solutions to certain important PDEs using a variety of techniques e.g. Green's functions, separation of variables. They should also be familiar with important analytic properties of the solution.
Content: Topics will be chosen from the following:
Elliptic equations in two independent variables: Harmonic functions. Mean value property. Maximum principle (several proofs). Dirichlet and Neumann problems. Representation of solutions in terms of Green's functions. Continuous dependence of data for Dirichlet problem. Uniqueness.
Parabolic equations in two independent variables: Representation theorems. Green's functions.
Self-adjoint second-order operators: Eigenvalue problems (mainly by example). Separation of variables for inhomogeneous systems.
Green's function methods in general: Method of images. Use of integral transforms. Conformal mapping.
Calculus of variations: Maxima and minima. Lagrange multipliers. Extrema for integral functions. Euler's equation and its special first integrals. Integral and non-integral constraints.
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Programme availability: |
MA30059 is Optional on the following programmes:
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- TSMA-AFM09 : MSc Mathematical Sciences
- TSMA-APM09 : MSc Mathematical Sciences
- TSMA-AFM08 : MSc Modern Applications of Mathematics
- TSMA-AWM14 : MSc Modern Applications of Mathematics
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics
- USMA-AFB05 : BSc(Hons) Statistics (Year 3)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
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