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PHY3036 : Partial Differential Equations

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
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal Lectures - Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion371:0037:00Completion of in course assignments/ examination revision
Guided Independent StudyIndependent study361:0036:00Preparation time for lectures, background reading, coursework review
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.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignment
Prob solv exercises2M10Coursework assignment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments 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.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists