This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review: ".... This carefully written textbook, the third English edition, contains substantial new developments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject." Roberto Plato (Siegen), Zentralblatt MATH 1205.65002.

This book stems from the long standing teaching experience of the authors in the courses on Numerical Methods in Engineering and Numerical Methods for Partial Differential Equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University of Bergamo (Italy) and Emory University (Atlanta, USA). It aims at introducing students to the numerical approximation of Partial Differential Equations (PDEs). One of the difficulties of this subject is to identify the right trade-off between theoretical concepts and their actual use in practice. With this collection of examples and exercises we try to address this issue by illustrating "academic" examples which focus on basic concepts of Numerical Analysis as well as problems derived from practical application which the student is encouraged to formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the authors in research project developed in collaboration with scientists of different fields (biology, medicine, etc.) and industry. We wanted this book to be useful both to readers more interested in the theoretical aspects and those more concerned with the numerical implementation.

La Matematica Numerica e elemento fondante del calcolo scientifico. Punto di contatto di diverse discipline nella matematica e nelle moderne scienze applicate, ne diventa strumento di indagine qualitativa e quantitativa. Scopo di questo testo e fornire i fondamenti metodologici della matematica numerica, richiamandone le principali proprieta, quali la stabilita, l'accuratezza e la complessita algoritmica. Nel contesto di ogni specifica classe di problemi vengono illustrati gli algoritmi piu idonei, ne viene fatta l'analisi teorica e se ne verificano i risultati previsti implementandoli con l'ausilio di programmi in linguaggio MATLAB. Ogni capitolo e integrato da esercizi e temi svolti, questi ultimi corredati da programmi MATLAB. Il volume e indirizzato principalmente agli studenti delle facolta scientifiche, con particolare attenzione ai corsi di laurea in Ingegneria, Matematica e Scienze dell'Informazione. L'enfasi posta sullo sviluppo di software lo rende interessante anche per ricercatori e utilizzatori delle tecniche del calcolo scientifico nei campi professionali piu disparati. La quarta edizione contiene numerose integrazioni in quasi tutti i capitoli. Diverse sezioni sono inoltre state rivisitate con lo scopo di rendere piu chiari concetti ed argomenti di considerevole complessita.

Ce livre constitue une introduction au Calcul Scientifique. Son objectif est de presenter des methodes numeriques permettant de resoudre avec un ordinateur certains problemes mathematiques qui ne peuvent etre traites simplement avec un papier et un crayon. Les questions classiques du Calcul Scientifique sont abordees: la recherche des zeros ou le calcul d'integrales de fonctions continues, la resolution de systemes lineaires, l'approximation de fonctions par des polynomes, la resolution approchee d'equations differentielles. La presentation de ces methodes est rendue vivante par le recours systematique aux environnements de programmation Matlab et Octave dont les principales commandes sont introduites progressivement. Tous les algorithmes sont presentes sous la forme de programmes. Ceci permet de verifier tres rapidement leurs proprietes theoriques, en particulier la stabilite, la precision et la complexite. La resolution de divers problemes, souvent motives par des applications concretes, fait l'objet de nombreux exemples et exercices. A la fin de chaque chapitre, une section presente des aspects plus avances et fournit des indications bibliographiques qui permettront au lecteur d'appronfondir les connaissances acquises. Le dernier chapitre est consacre a la correction des exercices proposes tout au long du livre"

Ce livre a pour but de presenter les fondements theoriques et methodologiques de l'analyse numerique. Une attention toute particuliere est portee sur les concepts de stabilite, precision et complexite des algorithmes. Les methodes modernes relatives aux themes suivants sont presentees et analysees en detail: resolution des systemes lineaires et non lineaires, approximation polynomiale, optimisation, integration numerique, polynomes orthogonaux, transformations rapides, equations differentielles ordinaires. Les techniques presentees sont illustrees par de nombreux tableaux et figures. Beaucoup d'exemples et de contre-exemples sont proposes pour permettre au lecteur de developper son sens critique. Une caracteristique principale du livre reside dans l'abondance des programmes MATLAB qui accompagnent toutes les methodes numeriques presentees et qui les illustrent par des applications concretes. Le lecteur detient ainsi tous les outils pour acquerir de solides connaissances theoriques et les appliquer directement sur ordinateur. Cet ouvrage s'adresse aux etudiants du second cycle des universites, aux eleves des ecoles d'ingenieurs et, plus generalement, a toutes les personnes qui pratiquent le calcul scientifique.

Aus den Rezensionen der englischen Auflage:

Dieses Lehrbuch ist eine Einfuhrung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewohnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Ubungsaufgaben sowie deren Losung prasentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code.

MATLAB select 2003, Issue 2, p. 50.

Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nutzliche Sammlung von MATLAB Funktionen fur die Losung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. ...]

Die Prasentation des Stoffs ist durchgangig gut und leicht verstandlich und beinhaltet Losungen fur die Ubungen am Ende jedes Kapitels. Als exzellenter Neuzugang fur Universitatsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Erganzung zu anderen MATLAB-basierten Buchern von grossem Nutzen sein. Alles in allem: Sehr empfehlenswert. Fur Studenten im Erstsemester wie fur Experten gleichermassen.

S.T. Karris, University of California, Berkeley, Choice 2003. "

Questo testo, che fa parte della collana UNITEXT - La matematica per il 3+2, contiene una raccolta di esercizi riferiti agli argomenti tipici di un corso di metodi analitici e numerici proposto in un corso di laurea in Ingegneria o in Matematica. Ogni paragrafo e preceduto da un breve richiamo delle principali nozioni di teoria necessarie affinche l'allievo possa risolvere gli esercizi proposti. La risoluzione della maggior parte degli esercizi si avvale della libreria MLife, sviluppata dagli autori, in linguaggio MATLAB. Questo consente l'immediata verifica da parte degli studenti delle principali proprieta teoriche introdotte.

Numerische Mathematik ist ein zentrales Gebiet der Mathematik, das f r vielf ltige Anwendungen die Grundlage bildet und das alle Studierenden der Mathematik, Ingenieurwissenschaften, Informatik und Physik kennenlernen.
Das vorliegende Lehrbuch ist eine didaktisch exzellente, besonders sorgf ltig ausgearbeitete Einf hrung f r Anf nger. Eines der Ziele dieses Buches ist es, die mathematischen Grundlagen der numerischen Methoden zu liefern, ihre grundlegenden theoretischen Eigenschaften (Stabilit t, Genauigkeit, Komplexit t)zu analysieren, und ihre Leistungsf higkeit an Beispielen und Gegenbeispielen mittels MATLAB zu demonstrieren. Die besondere Sorgfalt, die den Anwendungen und betreffenden Softwareentwicklungen gewidmet wurde, macht das vorliegende Werk auch f r Studenten mit abgeschlossenem Studium, Wissenschaftler und Anwender des wissenschaftlichen Rechnens in vielen Berufsfeldern zu einem unverzichtbaren Arbeitsmittel. Inhalt von Band 2 siehe ToC.

Offre una straordinaria varieta di problemi di interesse applicativo, metodi numerici, algoritmi, programmi, esercizi, illustrazioni e soluzioni Include 110 esempi, 160 esercizi risolti e 50 programmi Matlab e Octave Il capitolo iniziale richiama gli elementi di base di Analisi Matematica, di Algebra Lineare e di Matlab/Octave necessari per la comprensione di tutti gli altri capitoli