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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, 4 September 2017  
Tutorials: 
Monday 1011, and Wednesday 1011. Venue: AdB1020 . First tutorial: Monday, 18 Sep 2017. 

Labs:  Thursday 16.0016.50  
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. 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
See also the entry for MA385 on p209 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: 04/09/2017  
0.2 Taylor's theorem.  Start: 07/09/2017  annotated slides  
Section 1: Solving nonlinear equations  
Notes:  Solving nonlinear equations (complete!)  
Slides:  1.1 The bisection method.  Start: 11/09/2017  annotated slides 
1.2 The secant method.  Start: 14/09/2017  annotated slides  
1.3 Newton's method.  Start: 21/09/2017  annotated slides  
1.4 Fixed point iteration.  Start: 25/09/2017  annotated slides  
Lab 1:  1.5 Implementing the bisection and secant methods.  File: Bisection.m  
1.6 Wrap Up.  Start: 28/10/2017  (No annotated slides)  
Extra:  Making a Julia set with Matlab  
Assignment 1  Submit carefully written solutions and
(where appropriate) computer code, for Exercises 1.5, 1.6, 1.7, 1.11(a) and 1.12. A good grade depends on correctness and clarity. DEADLINE: 3pm, 5 Oct 2017 
Marking sheet used for grading. Solutions to selected exercises, and the subset of those that were Assignment Exercises. 

Section 2: Initial Value Problems (IVPs)  
Notes:  Initial Value Problems (complete)  
Slides:  2.1 Introduction to IVPs  Start: 02/10/2017  annotated slides 
2.2 Euler's method.  Start: 02/10/2017  annotated slides  
2.3 Analysis of Euler's method  Start: 05/10/2017  annotated slides  
2.4 Runge Kutta 2  Start: 12/10/2017  annotated slides  
Sample
test
Sample solutions to the sample test . Class test and outline solutions. 
19/10/2017  
Lab 2: 19+26/10/2017  Implementing Euler's method.  Files: Euler.m Euler_Solution.m  
2.6 Runge Kutta 4  Start: 23/10/2017  annotated slides  
2.7 From IVPs to Linear Systems  Start: 26/10/2017  No annotated slides.  
Extra:  Heat.m  Solving the heat equation in Matlab/Octave  
Lab 3: 9+16/11/2017  Implementing RK2 and RK3.  File: Euler_Solution.m  Deadline: 5pm, 17/11/17 
All the exercises from Section 2  
Section 3: Solving Linear Systems  
Notes:  Solving Linear Systems (complete)  (Just the exercises from Section 3)  
Slides:  3.1 Introduction to solving linear systems  Start: 02/11/2017  annotated slides 
3.2 Gaussian Elimination and Triangular Matrices  Start: 03/11/2017  annotated slides  
3.3 LUfactorisation  Start: 06/11/2017  annotated slides  
3.4 Solving Ax=b  Start: 13/11/2017  annotated slides  
Extra:  LUDet.m LUFactor.m BackSubs.m Test_LUFactor.m  
3.5 Vector and Matrix Norms  Start: 13/11/2017  annotated slides  
3.6 Condition Numbers  Start: 16/11/2017  annotated slides  
3.7 Gerschgorin's Circles  Start: 20/11/2017  annotated slides  
4.0: review of MA385  Start: 23/11/2017  Notes posted on Blackboard, under "Learning Materials... Review of MA385".  
Assignment 2  Please submit carefully written solutions to Exercises
2.13, 3.4, 3.9, and 3.10. DEADLINE: 09:00, Monday 20 November. If submitting your work on the deadline, then hand it in at the start of class. 
The homework exercises on a single sheet. The marking sheet for grading. Outline solutions to the homework exercises. 

All the notes for MA385(with hyperlinks) 
This schedule is tentative and subject to change.
MA385 Schedule (2017/2018)  

Week  Monday  Tuesday  Wednesday  Thursday  Friday  
Week 1 (4 Sep)  1st lecture: 910  
Week 2 (11 Sep)  
Week 3 (18 Sep)  Tutorial 1011  Tutorial 1011  
Week 4 (25 Sep)  Tutorial 1011 (TBC)  Lab 1  
Week 5 (2 Oct)  Tutorial  Assignment 1 due. Lab 1  
Week 6 (9 Oct)  Tutorial  Tutorial  
Week 7 (16 Oct)  Lecture cancelled (Ophelia) 
Tutorial  Class test Lab 2 

Week 8 (23 Oct)  Tutorial  Lab 2  
Week 9 (30 Oct)  No lecture or tutorial (public holiday) 
Tutorial  
Week 10 (6 Nov)  Tutorial  Lab 3  
Week 11 (13 Nov)  Tutorial  Assignment 2 due Lab 3 

Week 12 (20 Nov)  Tutorial  Tutorial  
Study Week  
Exam Week 1  
Exam Week 2 