Course Details in 2021/22 Session

Module Title	LH Methods in Partial Differential Equations
School	Mathematics
Department	Mathematics
Module Code	06 27714
Module Lead	Dr Chris Good
Level	Honours Level
Credits	20
Semester	Semester 1
Pre-requisites	LI Differential Equations - (06 25670) LI Multivariable & Vector Analysis - (06 25667) LI Linear Algebra - (06 15552)
Co-requisites
Restrictions	None
Contact Hours	Lecture-46 hours Tutorial-10 hours Guided independent study-144 hours Total: 200 hours
Exclusions
Description	This module introduces the concept of partial differential equations, the concept of solution to partial differential equations, with initial and initial boundary value problems for evolution PDE, and steady state boundary value problems for steady state PDE. First order PDE and systems of first order PDE’s are considered (both linear and nonlinear) and solution methods are developed, with specific examples relating to linear and nonlinear simple wave PDE’s. General second order linear PDE are considered, and classified accordingly to canonical form in canonical coordinates. Second order linear hyperbolic, parabolic and elliptic PDEs are examined in general, and then in detail for the wave equation, the diffusion equation and Laplace’s equation. More general linear evolution PDE will also be considered. The solution methods with involve Fourier integral, Fourier series and Green’s Function approaches. Uniqueness will be established in all cases. Specific nonlinear evolution PDE such as the Burger’s equation and Korteweg de Vries equation will be introduced and discussed.
Learning Outcomes	By the end of the module students should be able to: Appreciate PDE problems and understand the concept of classical solution to PDE problems. Students should be able to effectively employ the method of characteristics to construct solutions to PDE problems. For linear second order PDE problems, students should be able to construct the canonical coordinates and the canonical form and classify the PDE. For the wave equation, the diffusion equation and Laplace’s equation, students should be able to construct solutions to the Cauchy, Neumann and Dirichlety problems using Fourier Integral, Fourier series and Green’s Function methods. Students should also appreciate how to apply these methods to more general linear evolution PDE
Assessment	27714-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	2 hour Written Unseen January Examination (80%); In-course Assessment (20%).
Other
Reading List