IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
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IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
The Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ing-in-Publication DataBasmadjian. DiranThe art of modeling in science and engineering / Diran Basmadjian.p. cm.Includes bibliographical references and index.ISBN 1-58488-012-0I. Mathematical models. 2. Science—Mathematical models. 3. Engineering— Mathematical models. I. Title.QA401.B38 19995U’.8—dc IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 282199-11443CIPThis book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and souIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
rces are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the authoThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28r the purpose of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act. 1988. this publication may not be reproduced, stored or transmitted, in any form or by any means, electronic or mechanical, including photocopying, microfilming. and recor IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ding, or by any information storage or retrieval system, without the prior permission in writing of the publishers, or in the case of reprographic repIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
roduction only in accordance with the terms of the licenses issued by the Copyright Licensing Agency in the UK. or in accordance with the terms of theThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28 distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying.Direct all inquiries to CRC Press LLC. 2000 N.w. Corporate Blvd.. Boca Raton. Florida 33431.Trademark Notice: Product or corporate names may be tra IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28demarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.Visit the CRC Press Wei) site at wwIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
w.crcpress.com<0 1999 by Chapman & Hall/CRCNo claim to original U.S. Government works International Standard Book Number 1-58488-012-0Library of CongrThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28the ensemble of equations which describe and interrelate the variables and parameters of a physical system or process. The term modeling in turn refers to the derivation of appropriate equations that are solved for a set of system or process variables and parameters. These solutions are often referr IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ed to as simulations, i.e., they simulate or reproduce the behavior of physical systems and processes.Modeling is practiced with uncommon frequency inIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
the engineering disciplines and indeed in all physical sciences where it is often known as “Applied Mathematics.” It has made its appearance in otherThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ing slant to the contents of the book, but that discipline now reaches out. some would say with tentacles, far beyond its immediate narrow confines to encompass topics of interest to both scientists and engineers. We address the book in particular to those in the disciplines of chemical, mechanical, IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28 civil, and environmental engineering, to applied chemists and physicists in general, and to students of applied mathematics.The text covers a wide raIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
nge of physical processes and phenomena which generally call for the use of mass, energy, and momentum or force balances, together with auxiliary relaThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28re at a steady state. Thus, transport phenomena play an important but not exclusive role in the subject matter covered. This amalgam of topics is held together by the common thread of applied mathematics.A plethora of related specialized tests exist. Mass and energy balances which arise from their r IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28espective conservation laws have been addressed by Reklaitis (1983), Felder and Rousseau (1986) and Himmelblau (1996). The books by Reklaitis and HimmIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
elblau in particular are written at a high level. Force and momentum balances are best studied in texts on fluid mechanics, among many of which are byThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ird. Stewart, and Lightfoot (1960) remains unsurpassed. Much can be gleaned on dynamic or unsteady-systems from process control texts, foremost among which are those by Stephanopoulos (1984). Luyben (1990) and Ogunnaike and Ray (1996).In spite of this wealth of information, students and even profess IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ionals often experience difficulties in setting up and solving even the simplest models. This can be attributed to the following factors:• A major stuIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
mbling block is the proper choice of model. How complex should it be? One can always choose to work at the highest and mostto models of unmanageable cThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28f the solution. Constraints of time and resources often make it impossible to embark on elaborate exercises of this type, or the answer sought may simply not be worth the effort. It is surprising how often the solution is needed the next day. or not at all. Still, there are many occasions where PDEs IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28 are unavoidable or advantage may be taken of existing solutions. This is particularly the case with PDEs of the “classical” type, such as those whichIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
describe diffusion or conduction processes. Solutions to such problems are amply documented in the definitive monographs by Carslaw and Jaeger (1959)The Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28ons (ODEs) or even algebraic equations (AEs). The motto must therefore be “PDEs if necessary. but not necessarily PDEs.”•The second difficulty lies in the absence of precise solutions, even with the use of the most sophisticated models and computational tools. Some systems are simply too complex to IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28yield exact answers. One must resort here to what we term bracketing the solution, i.e.. establishing upper or lower bounds to the answer being soughtIT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28
. This is a perfectly respectable exercise, much practiced by mathematicians and theoretical scientists and engineers.•The third difficulty lies in maThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress Catalogi IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28in boldness and leap in imagination is called for. These are not easy attributes to satisfy.Overcoming these three difficulties constitute the core of The Art of Modeling. Although we will not make this aspect the exclusive domain of our effort, a large number of examples and illustrations will be p IT training the art of modeling in science and engineering with mathematica basmadjian 1999 06 28resented to provide the reader with some practice in this difficult craft.The Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress CatalogiThe Art of MODELING in SCIENCE and ENGINEERINGDiran BasmadjianCHAPMAN & HALƯCRCBoca Raton London New York Washington. D.c.Library of Congress CatalogiGọi ngay
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