Module: Partial Differential Equations

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Partial Differential Equations
Module Code	MS509
School	School of Mathematical Sciences
Module Co-ordinator	Semester 1: Paul Razafimandimby Semester 2: Paul Razafimandimby Autumn: Paul Razafimandimby
Module Teachers	Turlough Downes Paul Razafimandimby
NFQ level	9	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
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

Programme or List of Programmes

AMPD	PhD
AMPM	MSc
AMPT	PhD-track
BTPD	PhD
BTPM	MSc
BTPT	PhD-track
CHPD	PhD
CHPM	Master of Science
CHPT	PhD-track
GTSH	Graduate Training Visitor Program (S&H)
HHPD	PhD
HHPM	MSc
HHPT	PhD-track
IFPFIM	Pre-Masters Intl. Foundation Programme
MSAR	MSc in Astrophysics and Relativity
NSPD	PhD
NSPM	MSc
NSPT	PhD-track
PHPD	PhD
PHPM	MSc
PHPT	PhD-track
PYPD	PhD
PYPM	Master of Science
PYPT	PhD-track
SSPD	PhD
SSPM	MSc
SSPT	PhD-track

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