Linear Partial Differential Equations - MA5505

Location Term Level Credits (ECTS) Current Convenor 2019-20
Canterbury Autumn
View Timetable
5 15 (7.5)


Pre-requisite: MAST4006: Mathematical Methods 1, MAST4007: Mathematical Methods 2





In this module we will study linear partial differential equations, we will explore their properties and discuss the physical interpretation of certain equations and their solutions. We will learn how to solve first order equations using the method of characteristics and second order equations using the method of separation of variables.

Introduction to linear PDEs: Review of partial differentiation; first-order linear PDEs, the heat equation, Laplace's equation and the wave equation, with simple models that lead to these equations; the superposition principle; initial and boundary conditions

Separation of variables and series solutions: The method of separation of variables; simple separable solutions of the heat equation and Laplace’s equation; Fourier series; orthogonality of the Fourier basis; examples and interpretation of solutions

Solution by characteristics: the method of characteristics for first-order linear PDEs; examples and interpretation of solutions; characteristics of the wave equation; d’Alembert’s solution, with examples; domains of influence and dependence; causality.


This module appears in:

Contact hours

42 hours

Method of assessment

80% Examination, 20% Coursework

Indicative reading

T. Myint-U, L. Debnath, Linear Partial Differential Equations for Scientists and Engineers, Birkhäuser 2007 (online)
L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, 3rd edition, Birkhäuser 2012 (online)
E. Kreyszig, Advanced Engineering Mathematics, Wiley 2011

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within linear partial differential equations (PDEs);
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: separation of variables, Fourier series, the method of characteristics;
3 apply the concepts and principles in basic linear PDE methods in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.

The intended generic learning outcomes.
On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.

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