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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)

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


Students


Photo of Mohammed Abdulameer
Mohammed Abdulameer
(Leicester)
Photo of Faizah Al Omari
Faizah Al Omari
(Manchester)
Photo of Walid Almalki
Walid Almalki
(Cardiff)
Photo of Ahmed Alshehri
Ahmed Alshehri
(Cardiff)
Photo of Marton Benedek
Marton Benedek
(Southampton)
Photo of Kai Cao
Kai Cao
(Leeds)
Photo of Bwebum Cleofas Dang
Bwebum Cleofas Dang
(*External)
Photo of Jonathan Deakin
Jonathan Deakin
(Manchester)
Photo of Andrea Foiniotis
Andrea Foiniotis
(Surrey)
Photo of Danny Groves
Danny Groves
(Cardiff)
Photo of Hattie Hall
Hattie Hall
(Southampton)
Photo of Ying Huang
Ying Huang
(Surrey)
Photo of Ashkan Javaherian
Ashkan Javaherian
(Manchester)
Photo of Abdul Jumaat
Abdul Jumaat
(Liverpool)
Photo of Fadi Kahwash
Fadi Kahwash
(Northumbria)
Photo of MATTHEW LEWIS
MATTHEW LEWIS
(Cardiff)
Photo of Yu Liu
Yu Liu
(Loughborough)
Photo of Georgia Lynott
Georgia Lynott
(Manchester)
Photo of Michael Marnell
Michael Marnell
(Cardiff)
Photo of Daniel Miller
Daniel Miller
(Exeter)
Photo of Naoko Miyajima
Naoko Miyajima
(Durham)
Photo of HoangXuan Nguyen
HoangXuan Nguyen
(Northumbria)
Photo of Alexander Owen
Alexander Owen
(Exeter)
Photo of Alex Paterson
Alex Paterson
(Exeter)
Photo of Walton Pereira Coutinho
Walton Pereira Coutinho
(Southampton)
Photo of Courtney Quinn
Courtney Quinn
(Exeter)
Photo of Michael Roberts
Michael Roberts
(Liverpool)
Photo of Leonardo Rocchi
Leonardo Rocchi
(Birmingham)
Photo of Alex Safar
Alex Safar
(Cardiff)
Photo of Joe Siddons
Joe Siddons
(Liverpool)
Photo of Holly Smith
Holly Smith
(Nottingham)
Photo of Damian Smug
Damian Smug
(Exeter)
Photo of ANON STUDENT
ANON STUDENT
(*External)
Photo of Anthony Thompson
Anthony Thompson
(Liverpool)
Photo of Luan Trinh
Luan Trinh
(Northumbria)
Photo of Morgan Tudball
Morgan Tudball
(Loughborough)
Photo of Stephen Walsh
Stephen Walsh
(Leicester)
Photo of Duo Wang
Duo Wang
(Loughborough)
Photo of Anthony Williams
Anthony Williams
(Manchester)
Photo of Yifan Wu
Yifan Wu
(Manchester)
Photo of Michele Zadra
Michele Zadra
(*External)
Photo of Daoping Zhang
Daoping Zhang
(Liverpool)
Photo of Jiaju Zhou
Jiaju Zhou
(Loughborough)


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:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.)

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 (594.2 days ago)
Deadline: Friday 15 January 2016 (582.2 days ago)


Recorded Lectures


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