Academic Year: |
2014/5 |
Owning Department/School: |
Department of Mathematical Sciences |
Credits: |
6 |
Level: |
Honours (FHEQ level 6) |
Period: |
Semester 1
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Assessment Summary: |
EX 100% |
Assessment Detail: | |
Supplementary Assessment: |
MA30044 Mandatory Extra Work (where allowed by programme regulations)
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Requisites: |
Before taking this unit you must take MA20216 and take MA20219 and take MA20220 and take MA20223 |
Description: |
Aims & Learning Objectives: Aims: To furnish the student with a range of analytic techniques for the solution of ODEs and PDEs.
Objectives:
Students should be able to obtain the solution of certain ODEs and PDEs. They should also be aware of certain analytic properties associated with the solution e.g. uniqueness.
Content: Sturm-Liouville theory: Reality of eigenvalues. Orthogonality of eigenfunctions. Expansion in eigenfunctions. Approximation in mean square. Statement of completeness.
Fourier Transform: As a limit of Fourier series. Properties and applications to solution of differential equations. Frequency response of linear systems. Characteristic functions.
Linear and quasi-linear first-order PDEs in two and three independent variables: Characteristics. Integral surfaces. Uniqueness (without proof).
Linear and quasi-linear second-order PDEs in two independent variables: Cauchy-Kovalevskaya theorem (without proof). Characteristic data. Lack of continuous dependence on initial data for Cauchy problem. Classification as elliptic, parabolic, and hyperbolic. Different standard forms. Constant and nonconstant coefficients.
One-dimensional wave equation: d'Alembert's solution. Uniqueness theorem for corresponding Cauchy problem (with data on a spacelike curve).
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Programme availability: |
MA30044 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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