DCU Home | Our Courses | Loop | Registry | Library | Search DCU

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-ordinatorSemester 1: Turlough Downes
Semester 2: Turlough Downes
Autumn: Turlough Downes
Module TeachersTurlough Downes
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.



Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study137No Description
Directed learning3End 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 Assessment100% Examination Weight0%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class TestThe in-class test will test understanding of various methods of solving partial differential equations.40%Week 6
In Class TestAs previous in-class test.40%Week 11
In Class TestThis 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
AMPDPhD
AMPMMSc
AMPTPhD-track
BTPDPhD
BTPMMSc
BTPTPhD-track
CHPDPhD
CHPMMaster of Science
CHPTPhD-track
GTSHGraduate Training Visitor Program (S&H)
HHPDPhD
HHPMMSc
HHPTPhD-track
IFPFIMPre-Masters Intl. Foundation Programme
MSARMSc in Astrophysics and Relativity
NSPDPhD
NSPMMSc
NSPTPhD-track
PHPDPhD
PHPMMSc
PHPTPhD-track
PYPDPhD
PYPMMaster of Science
PYPTPhD-track
SSPDPhD
SSPMMSc
SSPTPhD-track
Archives:

My DCU | Loop | Disclaimer | Privacy Statement