文档介绍：Mathematical Modelling
Kluwer Texts in the Mathematical Sciences
VOLUME 28
A Graduate-Level Book Series
The titles published in this series are listed at the end of this volume.
Mathematical
Modelling
Case Studies and Projects
by
Jim Caldwell
City University of Hong Kong,
Kowloon, Hong Kong, . China
and
Douglas . Ng
City University of Hong Kong,
Kowloon, Hong Kong, . China
KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: 1-4020-1993-9
Print ISBN: 1-4020-1991-2
©2004 Kluwer Academic Publishers
New York, Boston, Dordrecht, London, Moscow
Print ©2004 Kluwer Academic Publishers
Dordrecht
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Kluwer Online at:
and Kluwer's eBookstore at: http://ebooks.
Jim Caldwell would like to dedicate this book to:
Ann, Janice, Clare and Simon Caldwell, and
Kei Shing Ng would like to dedicate this book to
his parents for giving him life and support.
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TABLE OF CONTENTS
Preface ix
Introduction 1
Part I Ordinary Differential Equations 5
Case Study A1
Deterministic Model in Contagious Disease 7
Case Study A2
ic Forces in High Field Coils 25
Project B1
Mass Balance of a Reactor in Steady State 39
Project B2
The Free and Forced Vibration of an Automobile 55
Project B3
Cantilever Beam Subjected to an End Load 67
ODE Problems 85
Part II Partial Differential Equations 91
Case Study A3
Cylindrical and Spherical Solidification in Heat Transfer 93
Case Study A4
Elastic Analysis of a Square Plate with Circular Holes 111
vii
viii
Project B4
Motion of Fluid Layers 127
Project B5
Mass Balance of a Reactor with Time Dependency 137
Project B6
Flow through Porous Media 147
PDE Problems 161
Part III Optimizat