Differential Equations (VS1) (U01920)

? Credit Points : 10 ? SCQF Level : 9 ? Acronym : MAT-3-DEs

Syllabus summary: Fourier transform, Power series and differential equations, systems of ODEs, separation of variables, orthogonal expansions and applications.

Entry Requirements

? This course is only available to part year visiting students.

? This course is a variant of the following course : U03107

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 3 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Thursday	12:10	13:00	KB

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