Module: Partial Differential Equations

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Partial Differential Equations
Module Code	MS509 (ITS) / MTH1068 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Paul Razafimandimby
Module Teachers	-
NFQ level	9	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None
Formal Exam

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

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.

Assessment Breakdown
Continuous Assessment	100%	Examination Weight	0%

Type	Description	% of total	Assessment Date
Course Work 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: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

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,

Other Resources

None