MAGIC066: Numerical Analysis

Course details

A core MAGIC course


Autumn 2013
Monday, October 7th to Saturday, December 14th


Live lecture hours
Recorded lecture hours
Total advised study hours


09:05 - 09:55
11:05 - 11:55


This course gives a broad introduction to Numerical Analysis and Scientific Computing. It is aimed to all PhD students in Mathematics.


No prerequisites information is available yet.


1. Introduction and general overview.
2. Approximation Theory. The Fast Fourier transform. 3. Methods for solving systems of linear and nonlinear equations. Gauss elimination, pivoting. Cholesky factorisation. Conditioning and error analysis. Least squares solution, Schur decomposition, the QR and QZ algorithms. Iterative methods: Jacobi, Gauss-Seidel, SOR. The Conjugate Gradient Method. Krylov subspace methods: Arnoldi algorithm. Conjugate gradient method and GMRES.
4. Numerical methods for ODEs. Taylor series methods. Runge-Kutta methods. Multi-step methods. Boundary value problems: shooting methods, finite difference methods, collocation. Methods for conservative and stiff problems.
5. Numerical methods for PDEs. Finite difference methods for elliptic equations. Parabolic equations: explicit, implicit and the Crank-Nicolson methods. The Galerkin, finite element and spectral methods.


  • TP

    Prof Tim Phillips

    Cardiff University


Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.



The assessment for this course will be via a take-home paper which will be put online after the end of the course at the beginning of January. The deadline for the work to be completed is midnight, 19th January 2014. The intention is that a student who has studied throughout the term will be able to pass by spending 2 hours on the exam. Successful completion of the assessment requires a mark of at least 50%.

Assessment not available

Assessments are only visible to those being assessed for the course.


Only consortium members have access to these files.

Please log in to view course materials.


Please log in to view lecture recordings.