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If you are looking for the page for the current academic year, please see nuigalway.blackboard.com, or contact the module's lecturer. 
Lecturer:  Dr Niall Madden 

Lectures:  Monday at 11.00 Tuesday at 11.00 Wednesday at 12.00 Classes take place in ADB1020. 

Starts:  Monday, Sep 8, at 11.00.  
Lecture summaries:  see below.  
Credits:  10 ECTS (a 5 ECTS variant may be available to students in structured PhD programmes).  
Overview:  This module is concerned with the mathematics of algorithms for
the numerical solution of differential equations, mainly by finite
different methods. It is aimed at graduate students (taught Masters and structured PhD programmes) in mathematical and computational sciences. 
Except in very rare cases, it is not possible to solve differential equations by apolitical methods. The best one can do is generate approximate solutions using numerical algorithms. In this module, we mainly focus on the use of finite difference methods for ordinary and partial differential equations. The construction/derivation of these methods will be our initial focus. However, most of the effort will go into analysing the methods, and establishing rigorous error bounds. We'll also study their implementation in Matlab, though this will be mainly in support of our theoretical studies.
Through the semester, I'll use various texts. As I introduce a text, the details will be added below. Some of these are published by SIAM and are freely available to you online through NUI Galway's subscription to SIAM ebooks.
These are extremely brief accounts of what was discussed in class at each lecture. Please refer to your lecture notes.
Lecture 1:  Welcome to the Masters Programme, and to MA5001  11am, Monday, 08/09/14  
Lecture 2:  Approximation of derivatives  11am, Tuesday, 09/09/14  
Lecture 3:  Taylor's series  12pm, Wednesday, 10/09/14  
Lecture 4:  Introduction to finite difference methods  11am, Monday, 15/09/14  
Lecture 5:  Towards error analysis  11am, Tuesday, 16/09/14  Code: SimpleFD1.m 
Lecture 6:  Error analysis: Part 1  12pm, Wednesday, 17/09/14  
Lecture 7:  Norms (i)  11am, Monday, 22/09/14  Lecture notes 
Lecture 8:  Norms (ii): norms of matrices  11am, Tuesday, 23/09/14  Lecture notes 
Class 9:  More norms  12pm, Wednesday, 24/09/14  
Class 10:  Finite differences in Matlab (1).  11am, Thursday, 25/09/14  Class notes Code: Solve_FD.m Code: Test_FD.m 
Class 11:  Consistency + Stability ⇒ Convergence  11am, Monday, 29/09/14  
Class 12:  Convergence in the 2norm  11am, Tuesday, 30/09/14  
Class 13:  Convergence in the maxnorm  12pm, Wednesday, 01/10/14  
Class 14:  Maximum principles for differential equations  11am, Monday, 06/10/14  
Class 15:  Maximum principles for difference equations  11am, Tuesday, 07/10/14  
Class 16:  Neumann boundary conditions (1)  12pm, Wednesday, 08/10/14  
Class 17:  Neumann boundary conditions (2)  11am, Monday, 13/10/14  
Class 18:  General boundary value problems  11am, Tuesday, 14/10/14  
Class 19:  More on general BVPs  12pm, Wednesday, 15/10/14  
Class 20:  Elliptic BVPs in two dimensions  11am, Monday, 20/10/14  
Class 21:  A simple FEM for the Poisson problem  11am, Tuesday, 21/10/14  
Class 22:  Ordering the unknowns in a 2D FEM  12pm, Wednesday, 22/10/14  
Class 23:  Expressing finite difference methods using Kronecker products  11am, Tuesday, 28/10/14  
Problem Set 2  
Brief details of each class. 