SyDe312 - Numerical Methods
Stephen Birkett

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Linear Algebra
Numerical Methods
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Computational Mathematics
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Marcia Hadjimarkos

Instructor: Stephen Birkett

Teaching Assistants:
  Mubarak Al-Mutairi DC 2638, Ext. 7736   Abdul-Rahim Ahmad DC 2630, Ext. 6393
Faezeh Jahanmiri

This course provides a comprehensive introduction to the standard numerical techniques commonly used in obtaining solutions to engineering problems. The availability of powerful software packages which provide convenient implementations of these methods does not eliminate the need for a thorough understanding of principles and practice. An informed choice of method is often required to match a particular application at hand, and it is sometimes useful to be able to customize methods. While it is obviously possible to use a software package without knowledge of its technical basis, this is a risky business with numerical methods since unexpected and seemingly inexpicable problems can, and do, occur. Acquiring an in-depth working knowledge of numerical computation using Matlab software is a secondary objective of the course.

Course Listserv:

  Atkinson/Han, Elementary Numerical Analysis, 3rd Edition, Wiley, 2004   Exercises will be taken from the text. Publisher's student resources (m-files)

[Optional book] Gilat, MATLAB An Introduction with Applications, 2nd Edition, Wiley, 2005

This book is useful unless you are already a Matlab guru or hate learning software from a text, rather than on the fly [a personal choice].

Access to Matlab software is essential.

Two options are possible (one cheap and one expensive). Matlab is available on campus unix servers and may be accessed by dial-in from home after installing XWindows software, a licence for which can be purchased from the CHIP (cost $20). Alternatively Matlab software may be purchased from Mathworks, or various other sources, but it is expensive. A student version of Matlab is available to purchase for $99US. Further information about on campus resources can be found on the IST matlab site.


Some kind of calculator [NO RESTRICTION] is required for doing tests and the exam.
Outline: Most of the topics are covered in the text, with some re-arrangement and omission according to time constraints. Lecture notes will also be provided throughout the course as well as being posted in pdf format on the website for reference. After some preliminary material on numerical computation, errors, precision, and matlab, the five main course units will be: I. Linear algebra II. Root-finding and non-linear systems III. Curve-fitting and interpolation IV. Numerical differentiation and quadrature V. Integration of differential equations. Within this general outline we may adjust the detailed topics as we go along. Details and text references will be provided on the course webpage. Continuous feedback during the course is particularly welcome and helpful. By the way....if you're a little rusty on linear algebra you might like to get up to speed by reviewing it asap, before we start Unit I.

Grading Scheme:
Assignments (0%) + Tests (3@15%) + Final exam (55%)

Suggested problems will be assigned and posted on this site. You can get help with these in the tutorials, from TAs, or from me. The first line for efficient communication is email, and especially the course listserv which is a great resource for communal discussion. Solutions can be handed in at any time to a TA to get feedback. Solutions to all homework problems will be posted on the course webpage at appropriate times. Try them before looking at the solutions!

Questions will: (i) test your knowledge of the material presented in the lectures or assigned text topics, with an emphasis on understanding the concepts, not formal proofs; (ii) test your mastery of the techniques, as required to solve the assignment problems (at least one test problem will be very similar, if not the same as an assigned problem). Sophisticated Matlab syntax and programming will not be tested, but a good basic working knowledge of Matlab as you should acquire from doing the assignments will be assumed in the tests. Consequently, it is in your interest to make absolutely sure you understand and can do all the assigned problems and get help if you are having trouble. Learning this material is an experiential process and cramming for tests is definitely not a feasible numerical method for success. [Your benefit in terms of marks for assignments is indirect since you should do better on the tests if you can do them.] Test solutions will be posted.

Final Exam.
The exam will include questions based on all course units (0 to V). As for the tests, problems will focus on: (a) theoretical knowledge - understanding of the methods and issues etc. (b) calculation skills - [limited] application of the methods in hand-solution, and (c) practical problems - homework assignments, practical implementation of algorithms, knowledge of Matlab use, and so on.

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©2004 Stephen Birkett