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
Prerequisites  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 nondegenerate cases) using eigenpairs
2. Evaluation and application of matrix exponential (in nondegenerate cases)
3. Classification of planar linear systems (nondegenerate 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 PoincareBendixson Theorem
7. Acquaintance with basic partial differential equations and types of boundary conditions
8. Solution of firstorder 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. Selfadjoint 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 powerseries 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 
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 

