MAS3806 : Partial Differential Equations and Nonlinear Waves
- Offered for Year: 2018/19
- Module Leader(s): Dr Clive Emary
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semester 2 Credit Value:
To develop further the theory of partial differential equations, including methods of solution and more general results, with appropriate applications.
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.
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class test|
|Scheduled Learning And Teaching Activities||Lecture||5||1:00||5:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||1||24:00||24:00||Office hours/self study: studying, practising and gaining understanding of course material|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Drop-ins|
|Guided Independent Study||Independent study||3||2:00||6:00||Review of coursework assignments and course test|
|Guided Independent Study||Independent study||2||5:00||10:00||Preparation for coursework assignments|
Jointly Taught With
|PHY3036||Partial 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.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||2||M||5||Class test|
|PHY3036||Partial Differential Equations and Nonlinear Waves||2||N/A|
|Prob solv exercises||2||M||5||Coursework 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.