Mathematical Modelling Courses for Engineering Education

248 Pages·1994·10.84 MB·English

by  Yaşar Ersoy

Mathematical Modelling Courses
for Engineering Education
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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
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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.