MAS3806 : Partial Differential Equations and Nonlinear Waves

Semester 2 Credit Value: 10
ECTS Credits: 5.0


To develop further the theory of partial differential equations, including methods of solution and more general results, with appropriate applications.

Module Summary
Almost all studies of physical phenomena lead to partial differential equations (PDEs), which have been studied for over 250 years; they are at the heart of modern applied mathematics, physics and engineering. It was soon noticed that many very similar – often identical – equations arise in many and varied applications, all with correspondingly similar solutions and methods of solution. This module continues the study of differential equations undertaken at Stage 2, bringing all these ideas together, developing more general methods for first-order PDEs and touching on, and extending, the ideas of separation of variables for second-order PDEs. In addition, some of the standard results and theorems relating to classical PDEs will also be discussed. Examples of these equations, and methods of solution, will be taken from various practical, relevant and important applications.

Outline Of Syllabus

Classification and methods of solution for some classes of first-order partial differential equations, including the Cauchy problem, and Lagrange’s and the parametric methods of solution; the classification of second-order semi-linear PDEs; Charpit's method for fully nonlinear 1st order PDEs ; nonlinear waves with applications to traffic flow; solitons and shockwaves.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery124:0024:00Office hours/self study: studying, practising and gaining understanding of course material
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins
Guided Independent StudyIndependent study32:006:00Review of coursework assignments and course test
Guided Independent StudyIndependent study25:0010:00Preparation for coursework assignments
Jointly Taught With
Code Title
PHY3036Partial Differential Equations and Nonlinear Waves
MAS8806Partial Differential Equations and Nonlinear Waves
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1202A90N/A
Written Examination402M5Class test
Exam Pairings
Module Code Module Title Semester Comment
PHY3036Partial Differential Equations and Nonlinear Waves2N/A
MAS8806Partial Differential Equations and Nonlinear Waves2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module, as this is the best way to test understanding of the mathematical content. The written exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the (in class) coursework test allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose, as well as their primary summative purpose.

Reading Lists