Module: Partial Differential Equations

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Partial Differential Equations
Module Code	MTH1068 (ITS: MS509)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	9	Credit Rating	7.5

Description

This module introduces students to both the methods and underlying theory of solving partial differential equations. Students will become familiar with first order quasi-linear and second order linear partial differential equations. A selection of analytic techniques for solving some partial differential equations that frequently occur in applications will be given. This module provides both a platform for modelling with partial differential equations and an introduction to analysing the nature of these equations. In contract to MS309, a closely related module, students are expected to develop an ability to critique the various solution methods and to demonstrate a deep understanding of when and why they can be used.

Learning Outcomes

1. state and interpret relevant defintions related to partial differential equations.
2. utilise the main analytic solution techniques for partial differential equations.
3. distinguish between the various types of differential equations
4. interpret the characteristics of hyperbolic, parabolic and elliptic equations
5. assess which solution method is appropriate for the main classes of differential equations.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	No Description
Tutorial	12	No Description
Independent Study	137	No Description
Directed learning	3	End of semester exam
Total Workload: 188

Section Breakdown
CRN	11228	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Paul Razafimandimby	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	The in-class test will test understanding of various methods of solving partial differential equations.	40%	Week 6
In Class Test	As previous in-class test.	40%	Week 11
In Class Test	This in-class test will assess the student's ability to assess and interpret solution methods.	20%	Week 11

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

First Order Quasi-linear PDEs
Characteristics; weak solutions; shocks.

Second Order Linear PDEs
Initial and boundary value problems; characteristics; wave equation; Laplace's equation; heat equation.

Indicative Reading List

Books:

K.E. Gustafson: 0, Differential Equations and Hilbert Space Methods, Wiley,
Y. Pinchover and J. Rubinstein: 0, An Introduction to Partial Differential Equations, Cambridge U.P.,
I. Stakgold: 0, Green's Functions and Boundary Value Problems, Wiley,

Articles:
None

Other Resources

None