MATH3201     Advanced Methods of Scientific Computation     2002

1  Lecturer

To contact the lecturer outside lectures and tutorials, try office hours. Note though that many small matters (e.g. which questions are on an assignment) can be quickly settled on the phone or by Email. Email is frequently used in the Mathematics department, and will often get a reply within half a day.

Material related to the course can be found on the MATH3201 web page.
This can be conveniently found off the lecturer's home page or from the Mathematics department's home page

2  Objectives

The objective of this course is to learn how to use numerical methods to solve problems! After successfully completing the course students will be able to :-

• use modern computational methods to solve problems in four important areas of scientific computation,

• understand the derivation and analysis of these methods,

• understand the advantages and disadvantages of these methods,

• apply them appropriately to novel problems,

• present their solutions clearly using well written English, making effective use of computer graphics and tables.

3  Assumed Knowledge

Generally MATH2000 and MATH2200 are recommended. Students will need to know and perhaps revise:-

• Multivariate Calculus. Partial derivatives, the gradient, and the Jacobian matrix.    Two dimensional integration and change of variable (dx dy = r dr dq).

• Complex numbers. Cartesian and polar form, and z = e^iq).

• Linear Algebra. (Eigenvalues, eigenvectors, and the eigenvalue-eigenvector decomposition for symmetric and non-symmetric matrices).

• Statistics and Probability: The idea of a normal variable, means, variance, and independance. The normal distribution.

• Computer Skills: Basic Matlab commands to compute with matrices and vectors and to plot results.

It is assumed that students have a basic understanding of Matlab. Students who have not used Matlab before should discuss this with the lecturer.

4  Text

There is no set text. Course notes will be distributed for much of the material

5  Content

The course is divided into five sections.

1. Fourier Transforms. (9L)The Fourier Transform and its implementation via the Fast Fourier Transform. Applications in signal processing & CAT scans.

2. Numerical Linear Algebra. (9L) Orthogonal Factorizations. Solution of least squares problems. Calculation of eigenvalues and eigenvectors. Direct and iterative methods for sparse systems.

3. Spline Approximation (6L). B-splines. Least squares approximation and regularization.

4. Solution of Ordinary Differential Equations. (6L)  Adaptive methods. Implicit methods for stiff equations. The method of Lines

5. Monte Carlo Methods. (6L) Pseudo-random numbers and generators. Monte Carlo integration.

6  Matlab

Practical computing in Matlab is an important part of the course. Many algorithms will be explained with Matlab code; and all assignments will need to be done with Matlab.

Most students will have used Matlab before. Those who have not will have to learn Matlab very quickly at the beginning of the course. Folk who need to learn Matlab for the first time should do the preliminary Matlab assignment. This is a good way to become familiar with the most essential commands. To do this assignments students can use either of the two excellent online introductions

• The Mathematics Department's Introduction to Matlab. (Paper copies are available from Graeme Chandler.)

• The Chemical Engineering Department's guide to Matlab Programming

7  Times

Lectures:	Monday	3.00pm	Room 8-212
	Wednesday	9.00am	Room 8-212
	Friday	12.00noon	Room 8-212
Tutorials	TBA	1hr /week	?

Tutorials start in the second week.

8  Assessment

The assessment criteria for this subject are available at

                http://www.maths.uq.edu.au/~gac/math3201/math3201criteria.html

The final mark will be calculated by

• 50%    Four assignments on the first 4 parts of the course. The marks for the four assignments are weighted by the number of lectures given on the topic, i.e. 30%, 30%, 20%, and 20% respectively. The assignments are due on Monday of weeks 5, 8, 10, and 12.

• 50%    The final two hour closed book exam. (There will be no choice of questions in this exam. Calculators will not be permitted).

If students are having problems meeting deadlines (due to assignments in other subjects, inner turmoil etc), they must see the Lecturer before the assignment is due. Otherwise, extensions will be given only in unforseeable emergencies, and supporting documentation (eg. medical certificates) may be required.

Students should be familiar with the rules which relate to assessment in their degrees as well as general university policy as found in the Assessment Rules. These are all set out in the Programs Handbook 2002 or the web.

9  Supplementary examinations

In some programs, supplementary examinations may be awarded to students who fail their major examinations (generally with a grade of 2 or 3). You should check the program rules for your degree program for information on the possible award of supplementary examinations. Applications for supplementary examinations must be made to the Director of Studies in the Faculty.

10  Special examinations

If a student is unable to sit a scheduled examination for medical or other adverse reasons, she/he can and should apply for a special examination. Applications made on medical grounds should be accompanied by a medical certificate; those on other grounds must be supported by a personal declaration stating the facts on which the application relies; other corroborative evidence may also be accepted.

Applications for special examinations for central exams must be made to the Director of Studies in the Faculty. Applications for special examinations in departmental exams must be made to the course coordinator.

More information on the University's assessment policy may be found on the web

EPSA Faculty policy on the award of special and supplementary exams may be found at on the web

11  Students with disabilities

Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services.

12  Assistance for Students

Students with English language difficulties should contact the lecturer. Students with English language difficulties who require development of their English skills should contact the Institute for Continuing and TESOL Education on extension 56565.

The Learning Assistance Unit located in the Relaxation Block in Student Support Services. You may consult learning advisers in the unit to provide assistance with study skills, writing assignments and the like. Individual sessions are available. Student Support Services also offers workshops to assist students. For more information, phone 51704 or on the web
          http://www.sss.uq.edu.au/index.html.

13  Plagarism

The official University policy on plagarism is:-

``Plagiarism is the action or practice of taking and using as one's own the thoughts or writings of another (without acknowledgement). The following practices constitute acts of plagiarism and are a major infringement of the University's academic values:''

1. (a)  where paragraphs, sentences, a single sentence or significant part of a sentence which are copied directly, are not enclosed in quotation marks and appropriately referenced

2. (b)  where direct quotations are not used, but are paraphrased or summarised, and the source of the material is not acknowledged either by footnoting or other simple reference within the text of the paper

3. (c)  where an idea which appears elsewhere in print, film or electronic medium is used or developed without reference being made to the author o the source of that idea.

When a student knowingly plagiarises someone's work, there is intent to gain an advantage and this may constitute misconduct. Students are encouraged to study together and to discuss ideas, but this should not result in students handing in the same or similar assessment work. Do not allow another student to copy your work. While students may discuss approaches to tackling a tutorial problem, care must be taken to submit individual and different answers to the problem. Submitting the same or largely similar answers to an assignment or tutorial problem may constitute misconduct.''

As assignments are part of the course assessment, they must be the students' own work. If an assignment contains plagarised material, it is a violation of the University examination rules. Marks will be deducted if answers do not display independence. In extreme cases disciplinary action may be taken.

Students are expected to write their own computer code and to write out the answers themselves. Knowledge can be shared, but answers and computer code should not be copied. It is also plagarism to `rewrite' another student's answers paragraph by paragraph by expressing the same ideas in different words.

You are encouraged to share knowledge with other students; but you should never give your code or written answers to others.

• You could answer the following questions:- Can you explain the nurgin formula for me? How do you use the Matlab nurg command?

• You sould not agree to the following: Can you give me your code for question 3? Can you give me your write up for question 3?

14  Computing

Matlab can be used in the Mathematics Department's computer laboratories and in a number of computing laboratories around campus. A student version of Matlab is available for about $150.00 from the bookshop, and copies of Matlab can be borrowed from the University Library

The Mathematics Department's computing laboratories can be used any time there is not a class scheduled there. If a small class is scheduled there and there are spare PC's, the lecturer will usually be happy for other students to work quietly at the back of the room.

Student's enrolled in the course will have accounts and passwords emailed to their university email account in the first week. If there are problems, see Paul Shackel (67-545) bringing your student card as a means of identification.

15  Library contact

The liaison librarian for Maths is located in the Physical Sciences and Engineering Library in the Hawken Building and may be consulted for assistance in the course:-

Larah Seivl-Keevers, l.seivl-keevers@library.uq.edu.au, extension: 52367

16  References

Students may find the following books useful as references.

• W. Cheney and D. Kincaid; Numerical Mathematics and Computing, Brooks / Cole, 1988

• R.L. Burden, J.D. Faires; Numerical Analysis. 4^th ed. , PWS-Kent, 1988.

• K.E. Atkinson; An Introduction to Numerical Analysis, 2nd edn., Wiley, 1988.

• S.D. Conte , C. de Boor; Elementary Numerical Analysis: An algorithmic approach, McGraw-Hill, 1980

• A.L. Garcia; Numerical Methods for Physics, Prentice Hall 1994

• M.T Heath; Scientific computing : an introductory survey, McGraw-Hill 1997. Slides based on the book are available from

                      http://www.cse.uiuc.edu/heath/scicomp/notes.html

• W.H. Press et. al., Numerical Recipes in C: The art of scientific computation., Cambridge University Press, 1992. This is available online section by section from http://www.nr.com .

For unit I

• William L. Briggs &Van Emden Henson, The DFT : an owner's manual for the discrete Fourier transform, SIAM, 1995.

• Avinash C. Kak & Malcolm Slaney, Principles of computerized tomographic imaging, IEEE, 1988.

For unit II

• W.W. Hager; Applied Numerical Linear Algebra, 1988

For Unit III

• Paul Dierckx, Curve and surface fitting with splines, Oxford : Clarendon Press, 1995.