Undergraduate Course: Complex Variable & Differential Equations (MATH10033)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 20 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Core course for Honours Degrees involving Mathematics and/or Statistics; also available for Ordinary Degree students.
Syllabus summary: Power series and differential equations, systems of ODEs, separation of variables, orthogonal expansions and applications, analytic functions, contour integrals, Laurent series and residues and Fourier transform. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
1. Solution of a linear system (in non-degenerate cases) using eigenpairs
2. Evaluation and application of matrix exponential (in non-degenerate cases)
3. Classification of planar linear systems (non-degenerate cases)
4. Determination of stability and classification of an equilibrium of a planar nonlinear system, by linearisation
5. Graphic use of integral of a conservative planar system
6. Acquaintance with Poincare-Bendixson Theorem
7. Acquaintance with basic partial differential equations and types of boundary conditions
8. Solution of first-order linear pde with constant coefficients
9. Solution of the wave equation by change of variable, leading to d'Alembert's solution
10. Acquaintance with notions of existence and uniqueness by example
11. Separation of variables for wave equation (finite string) and Laplace's equation (disc)
12. Handling Fourier series as orthogonal expansions, with an inner product and projection operator
13. Self-adjoint linear differential operators and their elementary spectral properties
14. The notion of completeness
15. Power series solution about a regular points of an analytic ordinary differential equation
16. Power series solution of Bessel's equation of order 0
17. Solutions of the wave equation for a circular drum
18. Knowledge of basic properties of analytic functions of a complex variable, including power-series expansions, Laurent expansions, and Liouville's theorem
19. The idea of conformal mapping, use of fractional linear transformations
20. Knowledge of the fundamental integral theorems of complex analysis
21. Ability to use residue calculus to perform definite integrals
22. Knowledge of some of the relations between analytic functions and PDE, e.g. relation to harmonic functions, the maximum principle
23. Familiarity with the Fourier integral as a tool for the study of ordinary and partial differential equations.
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Assessment Information
| Examination 100% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
http://www.readinglists.co.uk |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | CVD |
Contacts
| Course organiser | Dr Maximilian Ruffert
Tel: (0131 6)50 5039
Email: M.Ruffert@ed.ac.uk |
Course secretary | Dr Jenna Mann
Tel: (0131 6)50 4885
Email: Jenna.Mann@ed.ac.uk |
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