SCQF Level: 10
Availability: Autumn, Advanced module
Course Prerequisite: MATU9M2
Credit Value: 20 (1 module)
The primary objective of the module is to explore both the qualitative and quantitative aspects of linear and nonlinear ordinary and partial differential equations. Model-building skills will be emphasised with the use of appropriate software packages.
At the end of this module the student should be able to:
A1: Linear differential equations, forced damped oscillator, resonance.
A2: Linear systems, classification of critical point, global behaviour.
A3: Nonlinear systems, linearization, predator-prey and competition models.
B1: Partial differential equations, classification of second order equations.
B2: The three classical partial differential equations: diffusion, Laplace and wave equations. Solution through separation of variables in Cartesian coordinates.
B3: Fourier series and solution of boundary value and initial value problems for partial differential equations.
Formulation of practical problems, investigative skills, experience with various software packages.
G. ZILL and M. R. CULLEN "Differential equations with boundary-value problems", 4e, ITP 1997, ISBN 0-534-95580-0.
D.K. ARROWSMITH, C.M. PLACE "Dynamical Systems: Differential Equations, Maps and Chaotic Behaviour", Chapman & Hall, 1991, ISBN 0412 090809
3 one-hour lectures and one 1.5 hour tutorial per week.
1/3 coursework (2 class tests) and 2/3 examination.