Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.
Prerequisites: MATH2015 OR MATH2038 OR MATH2047 OR MATH2048
Aims and Objectives
Having successfully completed this module you will be able to:
- Show logical thinking in problem solving.
- Understand similarity solutions and their applications.
- Solve linear ODEs and PDEs with the use of the Green's function method.
- Understand the concept of well-posedness.
- Understand the existence of weak solutions and shocks.
- Demonstrate knowledge and understanding partial differential equations and how they relate to different modelling situations
- Understand the concept of the symbol of a PDE and the resulting classification of PDEs.
Common linear PDEs and their boundary conditions
Cauchy data and the Cauchy-Kowalewski expansion
Weak solutions of linear PDEs
Classification of PDEs and PDE systems from their principal symbol
Scalar conservation laws and the Riemann problem
Generalised functions and the delta-function
Green's functions for ODEs
Green's functions and applications for Laplace, Poisson and Helmholtz equations
Green's functions and applications for the heat equation
Green's functions and applications for the the wave equation
Learning and Teaching
Teaching and learning methods
Teaching methods include:
- 12 tutorials in the form of problem classes
- Summary lecture notes, solutions to problems and mock examination paper available on the Blackboard site for the module
- Chalk and talk lectures
Learning activities include:
- Individual Study
- Working through problems set in lecture notes at the end of each chapter
- Working through mock exam paper and the coursework assignment
|Total study time||150|
Resources & Reading list
Lecture notes. The module is based on summary lecture notes which are provided. There is no recommended book, but some suggestions are contained in an information sheet handed out at the start of the module and available on blackboard.
STRAUSS W.. Partial differential equations.
LEVEQUE R.. Numerical Methods for Conservations Laws.
HOWISON S.. Practical Applied Mathematics.
OCKENDON J, HOWISON S, LACEY A & MOVCHAN A. Applied Partial Differential Equations.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Repeat type: Internal & External