Maple and Mathematica A Problem Solving Approach for Mathematics
The first book to compare the main two computer algebra systems (CAS), Maple and Mathematica used by students, mathematicians, scientists, and engineers. Both systems are presented in parallel so that Mathematica users can learn Maple quickly by finding t
- PDF / 2,690,700 Bytes
- 498 Pages / 439.37 x 666.142 pts Page_size
- 95 Downloads / 324 Views
Inna Shingareva Carlos Lizárraga-Celaya
Maple and Mathematica A Problem Solving Approach for Mathematics Second Edition
SpringerWienNewYork
Dr. Inna Shingareva
Department of Mathematics, University of Sonora, Sonora, Mexico
Dr. Carlos Lizárraga-Celaya
Department of Physics, University of Sonora, Sonora, Mexico
This work (with enclosed CD-ROM) is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks. Product Liability: The publisher can give no guarantee for all the information contained in this book. This does also refer to information about drug dosage and application thereof. In every individual case the respective user must check its accuracy by consulting other pharmaceutical literature. The use of registered names, trademarks, 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.
© 2007, 2009 Springer-Verlag / Wien Printed in Germany
SpringerWienNewYork is part of Springer Science + Business Media springer.at
Typesetting: Camera ready by the authors Printing and Binding: Druckerei Stürtz, 97080 Würzburg Printed on acid-free and chlorine-free bleached paper SPIN: 12689057 Library of Congress Control Number: 2009933349
ISBN 978-3-211-73264-9 1st edn. SpringerWienNewYork
ISBN 978-3-211-99431-3 2nd edn. SpringerWienNewYork
To our parents, with inifinite admiration, love, and gratitute.
Preface
In the history of mathematics there are many situations in which calculations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number π began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated π (e.g., Archimedes, Ptolemy, Vi`ete, etc.). The first formula for computing decimal digits of π was discovered by J. Machin (in 1706), who was the first to correctly compute 100 digits of π. Then many people used his method, e.g., W. Shanks calculated π with 707 digits (within 15 years), although due to mistakes only the first 527 were correct. For the next examples, we can mention the history of computing the fine-structure constant α (that was first discovered by A. Sommerfeld), and the mathematical tables, exact solutions, and formulas, published in many mathematical textbooks, were not verified rigorously [25]. These errors could have a large effect on results obtained by engineers. But sometimes, the solution of such problems required such technology that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to improve the results that a huma
Data Loading...
