 Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 1
|
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA30044 Mandatory Extra Work (where allowed by programme regulations) |
| 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).
|
Programme availability:
|
MA30044 is Optional on the following programmes:
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
- USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
- TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
Department of Physics
- USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 3
- USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 4
- USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
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