MAGIC066: Numerical Analysis

Course details

A core MAGIC course

Semester

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

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Thursdays
09:05 - 09:55
Fridays
11:05 - 11:55

Description

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

Prerequisites

No prerequisites information is available yet.

Syllabus

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.

Lecturer

  • TP

    Prof Tim Phillips

    University
    Cardiff University

Bibliography

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Assessment

Description

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%.

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Files

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Lectures

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