Partial Differential Equations

Announcements:

Partial differential equations (PDE's) are used in most forms of mathematical modelling. Such as in finance, biology, quantum mechanics, general relativity and weather prediction to name a few. This course explores the analytic properties of PDE's , solutions techniques, uniqueness and existence theorems. Classical equations such as the Poisson, heat and wave equations, are analysed in detail. Concepts such as boundary and initial-boundary value problems, maximum principles, separation of variables, Fourier series, Green's functions, numerical methods, transform and variational methods are introduced.

Prerequisites

A first course in ordinary differential equations (MATA 2644) on the level of A first Course in Differential Equations - Dennis G Zill.

Dynamical Systems (MATA 3784) on the level of Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry and engineering. Stephen Strogatz. or Non-linear ordinary differential equations. DW Jordan and P Smith 2nd Ed Claredon advised.

Lecturer

Jeandrew Brink, Contact: BrinkJ2@ufs.ac.za , WWG 109

Course Material

Notes, articles assignments posted on this webpage.

The Part on first order systems will come from Fritz John Partial Differential equations.

For second order system we will use in part Course notes and Partial Differential Equations for Scientists and Engineers Stanley J. Farlow

Good references

Partial Differential Equations of Applied Mathematics 3rd Ed. Erich Zauderer 978-0471690733

Partial Differential Equations: 2nd Ed. L C Evans 978-0821848593

Partial Differential Equations 4th Ed. Fritz John 978-0387906096

Partial Differential Equations in Action: From Modelling to Theory (UNITEXT) 3rd Ed. Sandro Salsa 978-3319312378

Partial Differential Equations for Scientists and Engineers Reprint Edition by Stanley J. Farlow (Author) 978-0486676203

http://www.math.toronto.edu/ivrii/PDE-textbook/PDE-textbook.pdf (Also useful with nice examples but does contain typos.)

Lectures and Consultation Hours

Lecture 1: Tuesday 9.10 pm -11pm WWG119

Lecture 2: Wednesday 11.10 am -13am WWG 119

Consultation: Immediately after any class WWG 109

Evaluation

There are 2 semester tests: which each count 35 % of the semester mark. The tutorials make up the remainder of the semester mark, namely 30 %.

The semester tests are scheduled for :

Semester Test 1 ~ Tuesday 11 April 9-11

Semester Test 2 ~ Tuesday 23 May 9-11

A semester mark of 45% or more must be attained to gain admission to the exam. An exam mark of at least 40 % must be attained to pass the course.

In the final mark, the semester mark and exam result are weighted evenly. A final mark of at least 50 % must be attained to pass the course.

Grading Policy

No tutorials will be accepted after the due date. Hard copies must be handed in for grading. No scanned or emailed homework copies will be accepted.

In the unfortunate circumstance of missing a semester test, the lecturer must be notified within 24 h. In the case of illness, a doctors certificate must be provided. A make up / special test, may be oral and/or written and will cover all the semesters work.

Great emphasis is placed on original, creative work. A well argued, understood, possibly numerically ''wrong'' answer is of much better value than one copied from the web. Collaboration on homework sets is allowed provided collaborators are given credit, and the person handing in the answer can defend the reasoning. If other sources are used, such as, books, articles etc they must be referenced. Should plagiarism be suspected, a student will be asked to solve a similar problem on the blackboard during a consultation session, to obtain the marks for the tutorial.