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General


This course is part of the MAGIC core.

Description

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

Semester

Autumn 2015 (Monday, October 5 to Friday, December 11)

Hours

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

Timetable

  • Thu 11:05 - 11:55
  • Fri 12:05 - 12:55

Prerequisites

No prerequisites information is available yet.

Syllabus

1. Introduction and general overview.
2. Approximation Theory, Polynomial Interpolation and Numerical quadrature.
3. Methods for solving systems of linear and nonlinear equations.
4. The Fast Fourier transform.
5. 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.
6. 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.

Lecturers


Tim Phillips (main contact)
Email PhillipsTN@cardiff.ac.uk
Phone (029) 208 74194
Interests Non-Newtonian fluid mechanics, computational fluid dynamics, numerical analysis
Photo of Tim Phillips
Agis Athanassoulis
Email agis.athanassoulis@le.ac.uk
Phone 07472475794
Photo of Agis Athanassoulis
Andrea Cangiani
Email Andrea.Cangiani@le.ac.uk
Phone (0116) 252 3889
Photo of Andrea Cangiani


Bibliography


An Introduction to Numerical AnalysisE Suli and D Mayers
Theory and Applications of Numerical AnalysisG M Phillips and P J Taylor
Numerical Mathematics and ComputingCheney and Kincaid
Numerical Linear AlgebraTrefethen and Bau


Note:

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Assessment



The assessment for this course will be via a single take-home paper in January, with 2 weeks to complete and submit online. There will be 4 questions and you will need to the equivalent of 2 questions to pass.

MAGIC066 Take Home Exam

Files:Exam paper
Released: Monday 4 January 2016 (1075.3 days ago)
Deadline: Friday 15 January 2016 (1063.3 days ago)


Recorded Lectures


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