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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2011/2012
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Complex Variable & Differential Equations (MATH10033)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) Credits20
Home subject areaMathematics Other subject areaSpecialist Mathematics & Statistics (Honours)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic?No
Course descriptionCore 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.
Entry Requirements (not applicable to Visiting Students)
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
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2011/12 Full Year, Available to all students (SV1) WebCT enabled:  Yes Quota:  None
Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday
King's BuildingsLectureTh A, JCMB1-29 12:10 - 13:00
King's BuildingsLectureTh A, JCMB1-29 12:10 - 13:00
First Class Week 1, Monday, 12:10 - 13:00, Zone: King's Buildings. Th A, JCMB
Additional information Supervision: one hour per week (shared with other 'core' courses), at a time to be arranged with Supervisor.
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)3:00
Resit Exam Diet (August)3:00
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.
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
KeywordsCVD
Contacts
Course organiserDr Maximilian Ruffert
Tel: (0131 6)50 5039
Email: M.Ruffert@ed.ac.uk
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk
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© Copyright 2011 The University of Edinburgh - 16 January 2012 6:24 am