DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -- ARCHIVE as at 1 September 2013 for reference onlyTHIS PAGE IS OUT OF DATE

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Complex Variable & Differential Equations (MATH10033)

 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.
 Pre-requisites Students MUST have passed: ( Foundations of Calculus (MATH08005) AND Several Variable Calculus (MATH08006) AND Linear Algebra (MATH08007) AND Methods of Applied Mathematics (MATH08035)) OR ( Mathematics for Informatics 3a (MATH08042) AND Mathematics for Informatics 3b (MATH08043) AND Mathematics for Informatics 4a (MATH08044) AND Mathematics for Informatics 4b (MATH08045)) Co-requisites Prohibited Combinations Students MUST NOT also be taking Complex Variable (MATH10001) Other requirements None Additional Costs None
 Pre-requisites None Displayed in Visiting Students Prospectus? Yes
 Not being delivered
 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.
 Examination 100%
 None
 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
 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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