Where: Library, Computer Lab
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented MATLAB which extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary differential equations. This course will provide an introduction to using the Chebfun, and at the same time cover some of the fundamental aspects of approximation theory (Chebyshev approximation, barycentric interpolation, recursive zero-finding, etc, ...) which make it so powerful. We shall also describe how to solve differential equations in the system, and explore Chebfun2, the new 2-dimensional extension to the system. The course will culminate in mini-projects (with presentations), with the aim of using Chebfun to solve some problem related to the student's own area of interest. For the mathematical foundations of Chebfun, see Trefethen's "Approximation Theory and Approximation Practice" (www.chebfun.org/ATAP/) and for examples of what Chebfun can do, see our online collection at www.chebfun.org/examples/ Here's a link to Cleve Moler's book:http://www.mathworks.co.uk/moler/chapters.html
Alex Townsend
Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, England http://people.maths.ox.ac.uk/townsend)
Nick Hala
Dr Nick Hale Post-Doctoral Research Assistant, OCCAM Non-Stipendiary Lecturer, St Hugh's College, Oxford Tutor, Merton College, Oxford My current research interests are in adaptive spectral methods for numerical solutions of PDEs. These methods combine complex analysis, barycentric interpolation, and conformal mapping. This topic was central to my Oxford DPhil thesis, and I am continuing this working during my Post-Doc in OCCAM. I am heavily involved in the open-source Chebfun project, and was a lead developer of version 3. Since the release of version 4 I have been part-funded by The MathWorks as the director of the project. Chebfun is a software system written in object-oriented MATLAB, which extends familiar powerful methods of numerical computation to continuous or piecewise-continuous functions. One of its key aims is to provide a link between symbolic and numeric computing. You can find out more at www.chebfun.org I also have an interest in the application of conformal mapping to quadrature methods, and the computation of certain matrix functions by complex contour integrals. I completed by DPhil at St Hugh's College, in 2009, and currently hold a non-stipendiary lectureship teaching 2nd year Complex Analysis and Numerical Analysis. A copy of my CV can be found here, and my contact details in the link above.
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