LINEAR PDES - 2017/8

Module code: MAT2011

Module provider


Module Leader


Number of Credits


ECT Credits



FHEQ Level 5

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 2

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80%
School-timetabled exam/test IN-SEMESTER TEST 20%

Alternative Assessment


Prerequisites / Co-requisites

Calculus MAT1030, Ordinary Differential Equations MAT2007

Module overview

The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in details. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.

Module aims

The aim of this module is to study both qualitative and quantitative aspects of linear PDEs in one and two space dimensions. Students will be introduced to the very important method of characteristics and they will understand and use the method of separation of variables for solving initial-boundary value problems of linear PDEs.  The maximum principle will be proved and its power and importance in the analysis of solutions of PDEs conveyed to students.

Learning outcomes

Attributes Developed
 Classify linear PDEs and choose the appropriate method to solve them. C
Solve linear PDEs using the method of characteristics, Fourier transform, and separation of variables. C
Interpret solutions and critically relate them to physical settings. C
Understand the use of the maximum principle and energy methods for uniqueness and well-posedness. C

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

The contents of the module will include:

Linear PDEs: Examples, classification of PDEs and their physical interpretation. 
First-order and Second-order linear PDEs:  Method of characteristics.
Introduction to Fourier series and Fourier transform. Solution of initial and  boundary-value problems. Method of separation of variables.
The heat equation. The wave equation, d’Alembert’s solution.  Interpretation of solutions.
Laplace’s equation: mean-value theorem, maximum principle, Poisson formula.Existence and Uniqueness of solutions for the canonical PDEs. Energy methods.

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Present a detailed introduction to linear partial differential equations and the most common techniques for finding their solutions.
Give students experience (through demonstration) of the methods used to interpret, understand and solve problems in linear partial differential equations.


The learning and teaching methods include:

3 x 1 hour lectures per week x 11 weeks, with written notes to supplement the module handbook and Q + A opportunities for students.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·         Understanding of and ability to interpret and manipulate various methods for finding the solutions of linear partial differential equations. 

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the test and exam.


Thus, the summative assessment for this module consists of:

One two hour examination (three best answers contribute to exam mark) at the end of Semester 1; worth 80% module mark.

One in-semester test; worth 20% module mark.


Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments over an 11 week period.  In addition, verbal feedback is provided by the lecturer during tutorial lectures. 

Reading list

Reading list for LINEAR PDES :

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.