Calcul Scientifique: Cours, Exercices Corrigés Et Illustrations En MATLAB Et Octave
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Ce livre constitue une introduction au Calcul Scientifique. Son objectif est de présenter des méthodes numériques permettant de résoudre avec un ordinateur certains problèmes mathématiques qui ne peuvent être traités simplement avec un papier et un crayon. Les questions classiques du Calcul Scientifique sont abordées: la recherche des zéros ou le calcul d'intégrales de fonctions continues, la résolution de systèmes linéaires, l'approximation de fonctions par des polynômes, la résolution approchée d'équations différentielles. La présentation de ces méthodes est rendue vivante par le recours systématique aux environnements de programmation Matlab et Octave dont les principales commandes sont introduites progressivement. Tous les algorithmes sont présentés sous la forme de programmes. Ceci permet de vérifier très rapidement leurs propriétés théoriques, en particulier la stabilité, la précision et la complexité. La résolution de divers problèmes, souvent motivés par des applications concrètes, fait l'objet de nombreux exemples et exercices. À la fin de chaque chapitre, une section présente des aspects plus avancés et fournit des indications bibliographiques qui permettront au lecteur d'appronfondir les connaissances acquises. Le dernier chapitre est consacré à la correction des exercices proposés tout au long du livre
Alfio Quarteroni is full professor of Numerical Analysis at Politecnico di Milano, and of Modelling and Scientific Computing (CMCS) at EPFL (École Polytechnique Fédérale de Lausanne).
Since 2002 he is scientific director of MOX - Laboratory for Modeling and Scientific Computing of the Politecnico di Milano. Since 2010 he is director and founder of MATHICSE (Mathematical Institute of Computational Science and Engineering - at EPFL.
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