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Lecture notes  Schedule 
Lecturer:  Dr Niall Madden ADB1013, Arás de Brún Phone: 091 493803 Email: niall.madden@nuigalway.ie 

Lectures: 
Monday 9.0009.50 in AC201
Thursday 15.0015.50 in AC201 

First Lecture:  9.00, Monday, 10 September 2018  
Tutorials: 
Tuesday 1011 in AdBG021, and Friday 1011 in AC203. First tutorial: Tuesday, 25 Sep 2018. 

Labs:  TBA  
Course Content:  The Analysis of Numerical Methods. More details are given in the Course Description below.  
Assessment: 


Texts:  The main recommended text is: Suli and Mayers, An Introduction to Numerical Analysis (519.4 MAY). You can download the first chapter for free. In addition, an online version is available, free of charge, through the NUI Galway library. There are 8 hard copies in the library for you to borrow. In MA385, we will cover Chapters 1, 2, 5 and 12 (though not in that order).  
Additional texts:  G. W. Stewart, Afternotes on Numerical Analysis (519.4 STE ). Because NUI Galway subscribes to the SIAM ebook programme, full text is available through the library website.  
Cleve B. Moler, Numerical Computing with Matlab. Also freely available online.  
Course website:  Information and course documents will be posted here, and so on NUIGalway.Blackboard.com 
These course documents will include
MA385 (Numerical Analysis 1) is a one semester, 24 lecture, upperlevel module that emphasises the mathematics used to design numerical methods, and to analyse their properties. Students also experiment with implementing algorithms in Matlab/Octave. The course covers
Various applications of these methods will be presented, including financial modelling, and generating fractals.
See also the entry for MA385 on p194 of the Undergraduate Book of Modules
MA385 is followed by the Semester 2 module, MA378/MA531: Numerical Analysis II.
Table of contents for the notes thus far.  
Section 0: Introduction  
Notes:  Introduction to MA385. Taylor's Theorem  
Slides:  0.1 Introductory lecture.  Start: 10/09/2018  
0.2 Taylor's theorem.  Start: 13/09/2018  annotated slides  
Section 1: Solving nonlinear equations  
Notes:  Solving nonlinear equations (so far...)  
Slides:  1.1 The bisection method.  Start: 17/09/2018  annotated slides 
1.2 The secant method.  Start: 20/09/2018  annotated slides  
1.3 Newton's method.  Start: 27/09/2018  annotated slides  
1.4 Fixed point iteration.  Start: 01/10/2018  annotated slides  
1.5 Introduction to MATLAB.  
Lab 1:  1.6 Implementing the bisection and secant methods.  File: Bisection.m  
1.6 Wrap Up.  Start: 08/10/2018  (No annotated slides)  
Extra:  Making a Julia set with Matlab  
Assignment 1  Submit carefully written solutions to the
selected exercises.
A good grade depends on correctness and clarity. DEADLINE: 9am, Monday 15 October 
Marking sheet used for
grading. Solutions to selected exercises, including the assignment exercises. 

Section 2: Initial Value Problems (IVPs)  
Notes:  Initial Value Problems (complete)  
Slides:  2.1 Introduction to IVPs  Start: 11/10/2018  annotated slides 
2.2 Euler's method.  Start: 11/10/2018  annotated slides  
2.3 Analysis of Euler's method  Start: 15/10/2018  annotated slides  
2.4 Runge Kutta 2  Start: 18/10/2018  annotated slides  
2.5 Runge Kutta 4  Start: 22/10/2018  annotated slides  
Sample
test
Class test and outline solutions. 
05/11/2018  
2.6 From IVPs to Linear Systems  Start: 05/11/2018  annotated slides  
Extra:  Heat.m  Solving the heat equation in Matlab/Octave  
Lab 2: 6+9/11/2018  Implementing Euler's method.  Files: Euler.m Euler_Solution.m  Deadline: 5pm, 9 Nov 2018 
Lab 3: 13+16/11/2018  Implementing RK2  File: Euler_Solution.m  Deadline: 5pm, 23 November 2018 
All the exercises from Section 2  
Section 3: Solving Linear Systems  
Notes:  Solving Linear Systems (Complete!)  (All exercises from Section 3)  
Slides:  3.1 Introduction to solving linear systems  Start: 05/11/2018 (W091)  annotated slides 
3.2 Gaussian Elimination and Triangular Matrices  Start: 08/11/2018 (W092)  annotated slides  
3.3 LUfactorisation  Start: 12/11/2018 (W101)  annotated slides  
3.4 Solving Ax=b  Start: 19/11/2018 (W111)  annotated slides  
Extra:  LUDet.m LUFactor.m BackSubs.m Test_LUFactor.m  
3.5 Vector and Matrix Norms  Start: 19/11/2018 (W111)  annotated slides  
3.6 Condition Numbers  Start: 26/11/2018 (W121)  annotated slides  
3.7 Gerschgorin's Circles  Start: 26/11/2018  annotated slides  
4.0: Review of MA385  Start: 29/11/2018  Notes posted on Blackboard, under "Learning Materials... Review of MA385".  
Assignment 2  Please submit carefully written solutions to Exercises
2.10, 3.2, 3.5, 3.16 and 3.17. DEADLINE: 12.00, Monday 3 December (strict!). 
The marking sheet for grading. Outline solutions to the homework exercises.  
All the notes for MA385(with hyperlinks) 