Introduction to the Foundations of Applied Mathematics
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundament
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Mark H. Holmes
Introduction to the Foundations of Applied Mathematics Second Edition
Texts in Applied Mathematics Volume 56
Editors-in-chief A. Bloch, University of Michigan, Ann Arbor, USA C. L. Epstein, University of Pennsylvania, Philadelphia, USA A. Goriely, University of Oxford, Oxford, UK L. Greengard, New York University, New York, USA Series Editors J. Bell, Lawrence Berkeley National Lab, Berkeley, USA R. Kohn, New York University, New York, USA P. Newton, University of Southern California, Los Angeles, USA C. Peskin, New York University, New York, USA R. Pego, Carnegie Mellon University, Pittsburgh, USA L. Ryzhik, Stanford University, Stanford, USA A. Singer, Princeton University, Princeton, USA A. Stevens, Universität Münster, Münster, Germany A. Stuart, University of Warwick, Coventry, UK T. Witelski, Duke University, Durham, USA S. Wright, University of Wisconsin, Madison, USA
The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of computer modeling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The aim of this series is to provide such textbooks in applied mathematics for the student scientist. Books should be well illustrated and have clear exposition and sound pedagogy. Large number of examples and exercises at varying levels are recommended. TAM publishes textbooks suitable for advanced undergraduate and beginning graduate courses, and complements the Applied Mathematical Sciences (AMS) series, which focuses on advanced textbooks and research-level monographs.
More information about this series at http://www.springer.com/series/1214
Mark H. Holmes
Introduction to the Foundations of Applied Mathematics Second Edition
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Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, NY, USA
ISSN 0939-2475 ISSN 2196-9949 (electronic) Texts in Applied Mathematics ISBN 978-3-030-24260-2 ISBN 978-3-030-24261-9 (eBook) https://doi.org/10.1007/978-3-030-24261-9 Mathematics Subject Classification (2010): Primary: 76Axx, 76Bxx, 76Dxx 74Bxx, 74Dxx, 74Hxx, 74Jxx 74Axx, 34D05, 34E05, 34E10, 34E13, 35C06, 35C07, 35F50, 60J60, 60J65 1st edition: © Springer Science+Business Media, LLC 2009 © Springer Nature Switzerland AG 2019 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 exem
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