PHY3036 : Partial Differential Equations
- Offered for Year: 2022/23
- Module Leader(s): Dr Andrew Baggaley
- 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
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes – Synchronous On-Line |
| Guided Independent Study | Assessment preparation and completion | 37 | 1:00 | 37:00 | Completion of in course assignments/ examination revision |
| Scheduled Learning And Teaching Activities | Lecture | 22 | 1:00 | 22:00 | Formal Lectures - Present in Person |
| Guided Independent Study | Independent study | 36 | 1:00 | 36:00 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
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
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 2 | A | 80 | N/A |
Exam Pairings
| Module Code | Module Title | Semester | Comment |
|---|---|---|---|
| MAS3810 | Methods for Differential Equations & Partial Differential Equations & Non -Linear Waves | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 10 | Coursework assignment |
| Prob solv exercises | 2 | M | 10 | Coursework 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
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- PHY3036's Timetable