PHY3036 : Partial Differential Equations and Nonlinear Waves
- Offered for Year: 2020/21
- Module Leader(s): Dr Clive Emary
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value: | 10 |
ECTS Credits: | 5.0 |
Aims
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
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
Teaching Activities
Category | Activity | Number | Length | Student Hours | Comment |
---|---|---|---|---|---|
Scheduled Learning And Teaching Activities | Lecture | 4 | 1:00 | 4:00 | Present in Person |
Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Synchronous On Line Material |
Structured Guided Learning | Lecture materials | 18 | 1:00 | 18:00 | Non Synchronous Activities |
Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | N/A |
Structured Guided Learning | Structured non-synchronous discussion | 9 | 1:00 | 9:00 | N/A |
Scheduled Learning And Teaching Activities | Drop-in/surgery | 2 | 1:00 | 2:00 | Office Hour or Discussion Group Activity |
Guided Independent Study | Independent study | 47 | 1:00 | 47:00 | N/A |
Total | 100:00 |
Jointly Taught With
Code | Title |
---|---|
MAS3806 | Partial Differential Equations and Nonlinear Waves |
MAS8806 | Partial Differential Equations and Nonlinear Waves |
Teaching Rationale And Relationship
Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
Student should consult their individual timetable for up-to-date delivery information.
Assessment Methods
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
The format of resits will be determined by the Board of Examiners
Other Assessment
Description | Semester | When Set | Percentage | Comment |
---|---|---|---|---|
Written exercise | 2 | M | 20 | Written exercises |
Written exercise | 2 | A | 80 | Alternative Assessment |
Assessment Rationale And Relationship
A substantial formal test is appropriate for the assessment of the material in this module. The written exercises will consist of five exercises of approximately equal weight and will 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
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- PHY3036's Timetable