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Teaching computational science with computer algebra
Author(s) -
Gander Walter
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701004
Subject(s) - symbolic computation , computation , algebra over a field , construct (python library) , computer science , polynomial , function (biology) , series (stratigraphy) , differential (mechanical device) , theoretical computer science , algorithm , mathematics , calculus (dental) , pure mathematics , programming language , mathematical analysis , medicine , paleontology , dentistry , evolutionary biology , engineering , biology , aerospace engineering
Computer algebra systems can be used to generate algorithms for numerical computations. We have computed and shown examples in [1] and more recently in [2]. In this paper we emphasize the teaching aspect and use essentially the capability of computer algebra system to construct and manipulate the interpolating polynomial and to compute a series expansion of a function. We automatically generate formulas for integration with error terms and also generate multi‐step methods for integrating differential equations. Furthermore we discuss the use of multiple precision. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)