This course is organized by the NGSSC Graduate School.
It consists of five modules, the first three of which will be given at the
Department of Information Technology, Uppsala University,
and the last two
will be given at the Department of Computing Science, Umeå University.
As a part of the work to be done within the course, a self-study part is included, to take place during Week 2 (Jan 10-14) 2011.
Module I (Systems of linear equations):
In order to follow the material,
basic Linear Algebra concepts and definitions have to be reviewed:
vectors and matrices,
vector spaces, linear independence, rank of a matrix,
vector and matrix norms,
eigenvalues and eigenvectors, Gauss elimination. Recall also the notion of
numerical
error (absolute and relative) from your first course in Numerical Methods.
Module II (The Finite Difference method):
Refresh your knowledge on Partial and Ordinary Differential Equations.
One possibility is to consult the following two web-sources:
PDEs
and
ODEs .
Module III (Monte Carlo methods):
Refresh your basic knowledge in mathematical statistics e.g. from the book
R. J. Larsen, M. L. Marx, An Introduction to Mathematical Statistics and its
Applications, Prentice Hall, 1981,
or some other introductory text book. Of importance are concepts such as
random variable, probability density function, cumulative distribution function,
uniform and normal distributions,
central limit theorem.
An introduction to Monte Carlo methods is found in
G. Dahlquist, Å. Björck, Numerical Methods, Prentice-Hall, 1974, or Dover, 2003, ch 11.
Week | Date | Topic(s) | Time | Location |
---|---|---|---|---|
Module I: Systems of linear equations | ||||
3 | Jan 17 | ![]() |
9:15-12:00 | 1412 |
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13:15-17:00 | 1412 |
||
Jan 18 | ![]() |
9:15-12:00 | 1412 |
|
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13:15-17:00 | 1412 |
||
Module II: The Finite Difference Method | ||||
Jan 19 | ![]() |
9:15-12:00 | 1412 |
|
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13:15-17:00 | 1412 |
||
Jan 20 | ![]() |
9:15-12:00 | 1412 |
|
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13:15-17:00 | 1412 |
||
Module III: Monte Carlo methods | ||||
Jan 21 | ![]() |
9:15-12:00 | 1412 |
|
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13:15-17:00 | 1412 |
||
5 | Jan 24-28 | ![]() |
||
6 | Jan 31--Feb 4 | ![]() |
Recommended books
S.C. Charpa | Applied Numerical Methods with MATLAB for Engineers and Scientists |
McGraW-Hill International Edition, 2005. (Bacis level) |
J.H. Mathew, K.D. Fink | Numerical Methods Using MATLAB | Pearson Education International, 2004 (Basic level) |
W.Y. Yang, W. Cao, T.-S. Chung and J. Moris |
Applied Numerical Methods using MATLAB | J. Wiley & Sons Ltd, 2005. (Advanced level) |
Material to downloads
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here | Matlab codes and data | |
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here | Matlab codes and data | |
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here | Matlab codes | |
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here | Matlab codes | |
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here | Matlab code | |
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Organization issues:
Here are some instructions how to find us.