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MA 385/530 - Numerical Analysis (11/12)

Lectures summaries

Problem Sets

Other Stuff

Course Information

Lecturer:	Dr Niall Madden ADB-1013, Arás de Brún Phone: 091 524411 x3803 Email: niall.madden@nuigalway.ie
Class times:	Tuesday and Thursday, 14.10-15.00 in ADB 1020 (=C219)
First Lecture:	Tuesday, 4^th 2012
Tutorials: Lab:	Tuesday, 3pm. Alternate between labs and tutorials. Next class: Lab in the Friary Suite, 2pm 16/10/12
Office hour(s):	TBA
Course Content:	The Analysis of Numerical Methods. More details are given in the Course Description below.
Assessment:	Regular written homework and lab assignments, and a 2 hour exam at the end of semester
Texts:	The main recommended text is: Suli and Mayers, An Introduction to Numerical Analysis (519.4 MAY).
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 online from on-campus computers!
	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

Summary Lecture notes containing statements of proofs, exercises, etc, but not proofs or worked examples. These will available be several hours before the lecture. You should print them and bring them with you to lectures.
Problem sets
Important announcements, such as details on homework assignments, class test(s), tutorials, etc.
Links to useful and interesting websites.

Course Description

MA385 (Numerical Analysis 1) is a one semester, 24 lecture, upper-level undergraduate course 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

Newton's Method and other techniques for solving nonlinear equations;
Methods for solving initial value differential equations, such as Runge-Kutta methods;
Numerical methods for solving systems of linear equations and their analysis, including the role played by matrix norms;
Estimation of eigenvalues and eigenvectors (power method, Rayleigh quotient and Gerschgorin's circles).

MA385 is followed by the Semester 2 course MA378 - Numerical Analysis II, which will be taught by Emil Sköldberg

Lecture Summaries

1.	Tue 04/09/12	Lecture 1	Introduction to MA385/530.
2.	Thu 06/09/12	Lecture 2	Taylor Series.
3.	Tue 11/09/12	Lecture 3	Interval bisection
4.	Tue 12/09/12	Lecture 4	The secant method
5.	Tue 18/09/12	Lecture 5	From Secant to Newton
6.	Thu 20/09/12	Lecture 6	Analysis of Newton's method
7.	Tue 25/09/12	Lecture 7	Solving nonlinear problems with Matlab	Bisection.m
8.	Thu 27/09/12	Lecture 8	Wrap up of iterative methods	Julia.m
9.	Tue 02/10/12	Lecture 9	Initial Value Problems
10.	Thu 04/10/12	Lecture 10	One-step methods
11.	Tue 09/10/12	Lecture 11	Analysis of one-step methods
12.	Thu 11/10/12	Lecture 12	Runge-Kutta 2
13.	Tue 16/10/12	Lecture 13	Solving IVPs with Matlab	Euler.m
14.	Thu 18/10/12	Lecture 14	Higher-order methods
15.	Tue 23/10/12	Lecture 15	From IVPs to Linear Systems
16.	Thu 25/10/12	Lecture 16	Gaussian Elimination
17.	Tue 30/10/12	Lecture 17	Matlab 3: functions	SolveEuler.m, TestEuler.m.
18.	Thu 01/11/12	Lecture 18	Triangular matrices
19.	Tue 06/11/12	Lecture 19	LU-factorisation
20.	Thu 08/11/12	Lecture 20	Solving linear systems with LU-factorisation
21.	Tue 13/11/12	Lecture 21	Norms of vectors and matrices
22.	Thu 15/11/12	Lecture 22	Computing \|\|A\|\|₂
23.	Tue 20/11/12	Lecture 23	Condition numbers
24.	Tue 20/11/12	Lecture 24	Gerschgorin
		all the notes

Problem Sets

There will be several written assignments during the semester. These will be graded and returned to you. Along with the Matlab work, they will contribute 30% to the final grade for the course.

Problem Set 1. Submit carefully written solutions to the designated problems no later than 12th Oct '12.
Outline solutions to homework questions on Problem Set 1
Homework Set 2: submit solutions to Exercise 14.3 no later than Friday 16/11/11.
Outline solutions to homework questions on Problem Set 2
Problem Set 3. Submit carefully written solutions to the designated problems no later than 30 Nov 2012. Outline solutions to homework questions on Problem Set 3

Other stuff

NUI Galway has bought electronic access to books published by SIAM (Society for Industrial and Applied Mathematics). You can download the PDF for individual chapters from on-campus computers. Several of these books are directly relevant to this course:
- Learning Matlab, by Tobin A. Driscoll. A excellent primer if you are just starting to learn Matlab.
- Matlab Guide, by Desmond and Nicholas Higham is detailed and well-written. If you know a little Matlab, this is a great book to help you develop your skills and deepen you knoweldge.
- Numerical Computing with Matlab, by Cleve B. Moler. Nicely mixes Matlab programming with theory and algorithms of numerical methods.
- Afternotes on Numerical Analysis, by G.W. Stewart. Lectures 1-5 cover root-finding, and Lectures 9-16 deal with direct solution of linear systems. Other sections are covered in MA378
- Afternotes Goes to Graduates School, by G.W. Stewart. Lectures 10 and 11 cover Splines, a topic in MA378.
A video explaining the secant method.

School of Mathematics, Statistics and Applied Mathematics
National University of Ireland, Galway, University Road, Galway, Ireland.
Phone: +353 (0)91 492332 (direct) , +353 (0)91 524411 x2332 (switchboard)
Fax: +353 (0)91 494542 Email: Mary.Kelly@nuigalway.ie
This page was last updated Sunday, February 24