Mathematical Biology II: Spatial Models and Biomedical Applications
It has been over a decade since the release first edition of the now classic original edition of Murray's Mathematical Biology. Since then mathematical biology and medicine has grown at an astonishing rate and has established itself as a distinct discipli
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Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics. The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself. The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.
Interdisciplinary Applied Mathematics Volumes published are listed at the end of the book.
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J.D. Murray
Mathematical Biology II: Spatial Models and Biomedical Applications Third Edition
With 298 Illustrations
Springer
J.D. Murray, FRS Emeritus Professor University of Oxford and University of Washington Box 352420 Department of Applied Mathematics Seattle, WA 98195-2420 USA Editors S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected]
J.E. Marsden Control and Dynamical Systems Mail Code 107-81 California Institute of Technology Pasadena, CA 91125 USA [email protected]
L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA [email protected]
S. Wiggins School of Mathematics University of Bristol Bristol BS8 1TW UK [email protected]
c Alain Pons. Cover illustration: Mathematics Subject Classification (2000): 92B05, 92-01, 92C05, 92D30, 34Cxx Library of Congress Cataloging-in-Publication Data Murray, J.D. (James Dickson) Mathematical biology. II: Spatial models and biomedical applications / J.D. Murray.—3rd ed. p. cm.—(Interdisciplinary applied mathematics) Rev. ed. of: Mathematical biology. 2nd ed. c1993. Includes bibliographical references (p. ). ISBN 0-387-95228-4 (alk. paper) 1. Biology—Mathematical models. I. Murray, J.D. (James Dickson) Mathematical biology. II. Title. III. Series. QH323.5 .M88 2001b 2001020447 570 .1 5118—dc21 ISBN 0-387-95228-4
Printed on acid-free paper.
c 2003 J.D. Murray, c 1989, 1993 Springer-Verlag Berlin Heidelberg. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection
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