Mathematical Modelling Courses for Engineering Education NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and Kluwer Academic Publishers Physical Sciences Dordrecht, Boston and London o Behavioural and Social Sciences E Applied Sciences F Computer and Springer-Verlag Systems Sciences Berlin Heidelberg New York G Ecological Sciences London Paris Tokyo Hong Kong H Cell Biology Barcelona Budapest I Global Environmental Change NATo-pea DATABASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 30000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NA TO-PCO DATABASE compiled by the NATO Publication Coordination Office is possible in two ways: -via online FILE 128 (NATO-PCO DATABASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. -via CD-ROM "NATO Science & Technology Disk" with user-friendly retrieval software in English, French and German (© WTV GmbH and DATAWARE Technologies Inc. 1992). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. ~ Series F: Computer and Systems Sciences Vol. 132 Mathematical Modelling Courses for Engineering Education Edited by Ya$Clr Ersoy Department of Science Education Middle East Technical University TR-06531 Ankara, Turkey Alfredo O. Moscardini School of Computing and Information Systems University of Sunderland Sunderland SR1 3SD, UK Springer-Verlag Berlin Heidelberg GmbH Proceedings of the NATO Advanced Research Workshop on The Design of Mathematical Modelling Courses for Engineering Education, held in Izmir, Turkey, July 12-16, 1993 CR Subject Classification (1991): G.1.S, 1.1, 1.6, J.2, K.3 ISBN 978-3-642-08194-1 ISBN 978-3-662-02977-0 (eBook) DOl 10.1007/978-3-662-02977-0 CIP data applied for This work is subject to copyright. All rights are reserved. whether the whole or part of the material is concerned. specifically the rights of translation, reprinting. reuse of illustrations. recitation. broadcast ing, reproduction on microfilms or in any other way. and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1994 Typesetting: Camera ready by authors SPIN: 10130742 45/3140 -5 4 3 210 -Printed on acid-free paper Preface As the role of the modern engineer is markedly different from that of even a decade ago, the theme of engineering mathematics educa tion (EME) is an important one. The need for mathematical model ling (MM) courses and consideration of the educational impact of computer-based technology environments merit special attention. This book contains the proceeding of the NATO Advanced Research Workshop held on this theme in July 1993. We have left the industrial age behind and have entered the in formation age. Computers and other emerging technologies are penetrating society in depth and gaining a strong influence in de termining how in future society will be organised, while the rapid change of information requires a more qualified work force. This work force is vital to high technology and economic competitive ness in many industrialised countries throughout the world. Within this framework, the quality of EME has become an issue. It is expected that the content of mathematics courses taught in schools of engineering today have to be re-evaluated continuously with regard to computer-based technology and the needs of mod ern information society. The main aim of the workshop was to pro vide a forum for discussion between mathematicians, engineering scientists, mathematics educationalists, and courseware develop ers in the higher education sector and to focus on the issues and problems of the design of more relevant and appropriate MM courses for engineering education. It is an obselVed fact that recent developments in the field of both hardware and software have prOvided most mathematics in structors in the industrialised countries with the opportunity to fundamentally rethink their teaching approach and an opportunity to explore the potential of computer-based environments (CBE) in teaching and learning. Computers and computer-based technology help to release engineers from the drudgery of data capture, calcu lating, analysing, and formatting the results. The emerging tech nology will make it possible for the future engineer to devote much more time to thinking, abstraction, and generalisation. In the last two decades, therefore, there has been a great effort to integrate computers into the mathematics curricula in various institutions and to support numerous projects for various uses of computers and their implementation in higher education. Among others, there vi Math Modelling in Engineering Education is a general trend to inject computer algebra systems (CASs), e.g., Derive, Maple, Mathematica, etc., into the teaching of mathematics in the schools of engineering. We do hope that such trends will re sult in changes in how to teach as well as what to teach. Students can concentrate on understanding concepts in depth and be ex posed to real world problems. However, very little is known about how individuals learn mathematics and what environments are most productive in stimulating this learning. After getting together and exchanging ideas between researchers and academics whose work is concerned with teaching engineering mathematics, it was hoped that an agreement on how to revitalise EME by means of the CBE would be reached in the workshop. Among mathematics teachers, MM in the natural, applied, and social sciences is a favourite solution to the problem of how to use mathematics to solve rea11ife problems. However, there is no gen eral agreement on the most appropriate way to integrate MM in the existing courses in engineering curricula. Nevertheless, with the varied uses of computer and adequate software, it is now possible to provide new stimulating and relevant learning environments for either engineering science or MM courses, and prepare the stu dent-engineers for the future, not the past. In this connection, the aims in designing MM courses might be to make the mathematics materials seem more relevant, and equip students so that they can recognise and cope with situations in natural and engineering sci ences. One hopes that this type workshop, which is a co-operation be tween the members of NATO countries and some non-NATO coun tries, will seIVe as a model to help the less developed member countries further their EME. Overall, we believe that the workshop and the follow-up publications will substantially enhance our un derstanding of the use of CASs in MM courses, and will help to improve the learning and teaching of engineering mathematics. Alfredo O. Moscardini Ya!iar Ersoy University of Sunderland Middle East Technical University June 1994 Acknowledgements NATO has funded the workshop from which this book is an off spring. We thank the NATO ARW Committee for their support and positive attitude toward the theme discussed in the workshop. As always, many people contributed to the success of the work shop and to the potential success of this book. . For his contribu lion for the organisation of the workshop, we thank Professor Fred Simons. For their computer skills and tireless work on the manu script, we thank Petia Stoyanova and G. Alpay Ersoy. Further, to all the participants and the ideas they shared during the conference and in this book, we are truly thankful. Finally, most of the editing of this book was kindly supported by the METU during a part of Prof. Ersoy's sabbatical at the Univer sity of Sunderland, UK. Contents Introduction 1 Part I: Mathematical ModelllDg Issues 1. The Role and Practice of Mathematical Modelling in 7 Industry Today Mark Cross 2. The Teaching of Mathematical Modelling 17 Alfredo O. Moscardini 3. Using Maple in a Mathematical Modelling Course 33 Doug A. S. Curran and Walter Middleton 4. Design of Mathematical Modelling Courses for 59 Fluid Flow in Engineering Education Cahit Ciray Part II: EnglDeering Mathematics Education 5. Integrating New Information Technologies into 75 Engineering Mathematics Curricula y ~ar Ersoy and Alfredo O. Moscardini 6. Examples of Matlab in Engineering Education 83 Seppo Po7yolainen. Jan MultisUta and Kostadin Antchev 7. Issues Involved in Teaching Calculus with 93 Computer Algebra Systems Fred Simons 8. A Global Approach to Finite Element Method 113 Maria M. Cecchi and Enrico Secco x Math Modelling in Engineering Education 9. Finite Element Method by Using Mathematica 129 Mikhail D. MikhaUov 10. Ingmath: Software for Engineering Mathematics 153 Helmut Bausch 11. Power Series Solutions of ODEs 159 Harley Flanders 12. Comments on the Teaching of Computational 165 Fluid~arrrlcs AlanW.Bush Part m: Mathematical ModelHDg In Fluld Flow and Beat Transfer 13. Finite Difference Modelling of1\vo-Phase Flow 179 Instabilities in Boiling Systems Sadik Kaka.c and Venkat R. Mullur 14. Numerical Modelling in Heat Transfer by 211 Spectral Methods Mansour Zenouzi. Ywnan Yener and Andy Tangbom Part IV: Workshop A. Computer Algebra Systems in Mathematical 239 Education Fred Simons B. Mathematical Modelling in Fluid Flow 241 Alan W. Bush and Robert Mathhey Author and Subject Index 245 Introduction The engineering discipline has seen many changes in the twentieth centuty. At the beginning of the centuty, it was neatly classified into many branches, e.g., thennodynamics, electromagnetic theoty, fluid mechanics, heat transfer, mechanics, etc. In the last two dec ades, there is the beginning of a movement to recognise the com mon elements of these branches and thus to reunite the engineer ing field. These tendencies are apparent at university level by the number of universities that now run common first years to their engineering degrees, the introduction of mathematical modelling (MM) courses into the curricula, and the use of new computer technology and improved software. This book deals with MM and the use of new software in engineering education. The tenn mathematical modelling has many meanings yet once a definition is put forward, most scientists and engineers claim that that is what they have always done. The whole of engineering could be described as a prime example of MM. Yet MM is neither engi neering mathematics nor applied mathematics. Many people con fuse it with applied mathematics but again this is not so. It is to do with applying mathematics. Emphasis should be placed on the word applying as opposed to the adjective applied. Its importance as a diSCipline of study in its own right is still controversial and has only gained prominence over the last twenty years. Evidence for this is in the number of international confer ences which have been held during this period and international journals which have been published. However, the teaching of MM in schools and universities is still a lively subject for debate in sev eral countries and this issue is firmly addressed in Part One of this book. MM can be described as the process of translating real world problems into mathematical problems and interpreting the mathe matical solutions in tenns of the original problem. Real world problems seldom translate exactly into mathematical problems, there is always a degree of mismatch or error, and mathematical solutions however elegant are not always practical solutions. As such it often necessaty to ideallse or simplify the problem by making assumptions. The choice and use of assumptions is a key element of MM. Also important is the idea of iteration, i.e., the so lution is achieved by starting with a Simple model and gradually refining it, usually by adding features which were assumed unim portant in the original simple :fIrst model. In this sense, MM falls naturally into the area of problem solving.