Mathematical Foundations of Programming
The use of modern digital computers is indispensable for large numerical tasks. In the weather forecast linear systems of equations in thousands, even millions of unknowns, have to be solved in a short time.
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Einar Smith
Introduction to the Tools of Scientific Computing
Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick
Texts in Computational Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick
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More information about this series at http://www.springer.com/series/5151
Einar Smith
Introduction to the Tools of Scientific Computing
Einar Smith Fraunhofer Institut für Algorithmen und Wissenschaftliches Rechnen SCAI Sankt Augustin, Germany Institut für Numerische Simulation Rheinische Friedrich-Wilhelms-Universität Bonn Bonn, Germany
ISSN 1611-0994 ISSN 2197-179X (electronic) Texts in Computational Science and Engineering ISBN 978-3-030-60807-1 ISBN 978-3-030-60808-8 (eBook) https://doi.org/10.1007/978-3-030-60808-8 Mathematics Subject Classification (2010): 97N80 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. In contrast to widespread standard approaches, it does not focus on a specific language, but rather aims to explain the central underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and Matlab to Maple. This approach can best be illustrated with a recurring leitmotif: the numerical approximation of differential equations. In the basic Python chapter, we introduce the function concept and illustrate how derivatives can be approximated using discrete di
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