UNC Course description

The Essentials

ID	MATH566
Title	Introduction to Numerical Analysis
Times	MWF 12:00-12:50 PM, Phillips 301
Instructor	Sorin Mitran mitran (AT) amath.unc.edu
Office Hours	MWF 11:00-11:50 AM, Phillips 307
Description	Basic numerical methods, their mathematical analysis and computer implementation

Syllabus

Iterative methods
Interpolation: polynomial and spline approximations
Numerical differentiation and integration
Solution of ODEs and PDEs

Motivation and Objectives

Not all mathematical solutions can be expressed in closed, analytical form. Even when this is possible the analytical forms may be unwieldy. In such situations numerical methods offer an alternative that is widely used and the basis of the vast majority of current applications of mathematics in the sciences, engineering. This course introduces some basic methods in the context of real-life problems and presents the mathematical analysis of the methods as well as their implementation in Python.

Grading Policy

Homework - 1.2 x (10 assignments x (3 1-point exercises + a 2-point computer exercise) ) = 60 points
Midterm - 5 problems x 4 points = 20 points
Final - 5 problems x 4 points = 20 points
Extra credit - You can choose to draft a report on two of the following topics
- Rational interpolation = 5 points (report due 10/8)
- B-splines = 5 points (report due 10/8)
- Gauss-Legendre method for multiple integrals = 5 points (report due 12/5)
- High-order finite difference methods for two-point ODE boundary problem = 5 points (report due 12/5)

Mapping of point score to grades

		B+	84-88	C+	67-71	D+	51-55
A	96-	B	79-83	C	62-66	D	46-50
A-	89-95	B-	72-78	C-	56-61	F	0-45

Course Texts and Notes

Numerical Methods in Engineering with Python, Jaan Kiuslaas, Cambridge, 2005. $70.67 at amazon.com or $68.00 eBook.

Lesson Plan

Date	Text Section	Date	Text Section
8/22	1.1-1.3	10/15	6.1-6.2
8/24	1.4-1.7	10/17	6.2
8/27	4.1-4.2	10/22	6.3
8/29	4.3-4.4	10/24	6.4
8/31	4.5	10/26	6.4
9/5	SimpleIteration.pdf	10/29	OrthoPoly.nb Extra credit: 6.5, 7.1-7.2
9/7	4.5	10/31	RecursiveInt.pdf RecursiveInt.tm 7.2-7.3
9/10	3.1	11/2	7.3
9/12	3.2	11/5	7.4
9/14	3.2	11/7	7.5
9/17	4.7, 3.3	11/9	7.6
9/19	3.4	11/12	Finite element overview
9/21	Extra credit: 3.5, B-splines	11/14	Beam vibration experiment
9/24	5.1-5.2	11/16	8.1-8.2
9/26	5.3	11/19	8.3
9/28	5.4	11/26	2.2, 4.6
10/1	6.1-6.2	11/28	9.1-9.2
10/3	6.3	11/30	9.3
10/5	Midterm review	12/3	Final review
10/8	Midterm review	12/5	Final review
10/10	Midterm Examination MidtermSolution.pdf	12/10, 12:00 PM	Final Examination

Homework and Projects

Homework is due on Wednesday, not accepted after Friday, handed back the next Monday if turned in on time. It is preferred to present typeset answers to the 3 exercises, but handwritten solutions are accepted. The answer to the computer exercise must be typeset, the relevant code must be included along with tables and graphs presenting results.

Dates	Exercises	Computer work	Solution	Dates	Exercises	Computer work	Solution
8/22-8/29	Homework1	Item 4 from HW1	MATH566HW1sol.pdf	10/24-10/31	p.212: 1,3,4	p.213: 8
8/29-9/5	p.164:1,2,3	p.164: 7	MATH566HW2sol.pdf	11/5-11/26	MATH566HW7Revised.pdf	HW7Hint.pdf
9/5-9/19	p.121:1,4,7	p.122: 2 + apply Laguerre	Math566HW3sol.pdf	11/7-11/26	p. 266 1,2,3	p.267 10 (Runge-Kutta 4, adaptive time step)
9/19-9/26	p.119: Ex 3.5, p.120 Ex. 3.6, p.123, 10	p.124, 19 using Newton & spline	Math566HW4sol.pdf	11/19-11/30	p.307: 1,6, p.320:5	p.323: 17
9/26-10/3	p. 138: 6,7,8	p.140: 15	HW5sol.pdf	11/26-12/1	p.351:2,3,5	p.353: 10

When e-mailing homework, use subject line: MATH566 (Last Name) HWx

Scientific Computing Workstation

An immense amount of scientific computing software is freely available. As an introduction to what is available a virtual workstation environment has been prepared for this course. It is packaged as a VMWare 'virtual appliance'. To use this environment read instructions at this link: SciCompWorkstation.

In MATH566 we'll use a basic Xubuntu 7.04 Linux distribution with these additional packages:

Python with all scientific computation packages
TeXmacs and LaTeX
Fortran, C/C++ compilers
data visualization and plotting software

In order to reference this particular software environment we'll give it the name: SciPyWork.

You might wish to use commercial packages for which UNC has campus licenses. You are welcome to do so, but most of the capabilities of these packages are available in the free software provided in the SciPyWork, often in a more efficient way.

Here are some pointers on how to efficiently use this software.

Installing VMPlayer

Running Xubuntu

Using TeXMacs

Notes:

Important: As distributed in class the Xubuntu image requires 2 CPUs. Open the Ubuntu.vmx file from the directory where you unpacked the .zip file in a text editor (e.g. Notepad). Change the line numvcpus=2 to numvcpus=1.