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Deutsche Version ETH Zürich /Computer Science /Publications Search |
W. Gander and D. Gruntz, Institute of Scientific Computing, ETH Zürich
Language: | English |
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Pages: | 19 |
Available Files: | abstract plain Postscript gnu-compressed PS |
Abstract: | At ETH Zuerich we have redesigned our former courses on numerical analysis. We do not only run numerical programs but also introduce the students to computer algebra and make heavy use of computer algebra systems both in the lectures and the assignments. Computer algebra may be used to generate numerical algorithms, to compute discretization errors, to simplify proofs, etc., but also to run examples and to generate plots. We claim, that it is easier for students to follow a derivation which is carried out with the help of a computer algebra system than by hand. Computer algebra systems take over the hard hand work such as e.g. solving systems of equations. Students do not need to be concerned with all the details (and all the small glitches) of a manual derivation and can understand and keep the overview over the general steps of the derivation. A computer supported derivation is also more convincing than a presentation of the bare results without any reasoning. Moreover, using computer algebra systems rather complex numerical formulas can be derived, far more complex than what can be done in class by hand. E.g. all useful Newton-Cotes rules can be computed without problems, in contrast to hand derivations, which usually end with Simpson's rule. We will prove these statements with some examples taken from our introductory courses in scientific computing. We use Maple V Release 4, but the examples could also be reproduced e.g. with Mathematica, MuPad or any other computer algebra system. |
Jul . 1998
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