Bøger i European Consortium for Mathematics in Industry serien

The Fifth European Conference on Industrial Mathematics (ECMI 90) took place at Lahti, Finland on June 6-9, 1990. The conference was organised by the Rolf Nevanlinna Institute together with the Lahti Research and Training Centre of the University of Helsinki. Like its predecessors the Lahti meeting was devoted to the exchange of experience, ideas and methods from various fields of industrial mathematics. The series of ECMI conferences have clearly established an important forum of interaction between the advancing front of technology and one of its crucial development resources, modern applications-oriented mathematics. The precise title of the conferences has been the subject of some discussion and it has been argued that there is no such area which can be labelled as "industrial mathematics". This is certainly true if one thinks only in terms of the range of ideas, theorems, methods and algorithms constituting mathematics all of which may be applied. However with another viewpoint industrial mathematics is not a collection of topics but refers to the interactive process in which mathematics, the science, meets the real world of applications. Ideally this interaction involves both good mathematics and technological advance. The computer revolution has created a new era in technology with the increased computational capability to simulate complex industrial processes, devices, and other technolog­ making it possible ical systems. This simulation depends on mathematical modelling and analysis and these techniques, sometimes ingenious but often quite routine, have provided a powerful tool for industrial scientists and creative research management.

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1 Industrial Mathematics in Linz The Johannes-Kepler-University is situated in Linz, which is the industrial center of Austria. This location provides unique opportunities for cooperation between in­ dustry and a university which derives its name from one of the most eminent ap­ plied mathematicians of all times. The mathematics department was founded in the late Sixties, the first students graduated in 1974. In these boom times, they had no problems of finding jobs in industry. However, their employers were then more interested in their general training than in their specific mathematical skills. To change this, the department decided to actively seek cooperation with industry in what we called "problem seminars", where students were trained to solve (under guidance) real-world problems from local industry. Groundwork was already laid by a curriculum with special emphasis on numerical analysis, statistics, and optim­ ization. This work in problem seminars usually evolved into diploma theses. Inci­ dentally, in all projects presented here, students were involved at some stages. While the original motivation for cooperation with industry was educational, it turned out that most problems presented to us also led to interesting mathematical problems, so that nowadays our motivation is as much scientific as educational. When cooperating with industry, one cannot expect that the problems to be solved fall into one's special mathematical interest.

The sixth European Conference on Mathematics in Industry (ECMI 91) took place at Limerick, Ireland during August 27-31, 1991. This series of ECMI Conferences is clearly satisfying the need to provide a forum, in a European wide context, for the presentation of material related to the application of mathematics to industrial problems. The result, at Limerick, was the presence of approximately 170 delegates representing most countries of Western and Eastern Europe (with a small number from the U. S. and Canada) participating in this information exchange on a wide range of types of problems. The only identifiable common characteristic of the presentations was the element of application of mathematics to an industrially related problem. The conference programme consisted of 8 invited lectures with approximately 80 contributed papers. These proceedings consist of 7 invited lectures and 63 contributed papers. The range of topics is very wide including areas such as optical fibres, biomechanics, electric power optimization, heat conduction, cryptography, catalytic reactors, dynamics of non-Newtonian fluids, fluid dynamics in a variety of applications, continuing education, epidemiology, numerical methods and software, optimal control, robotics etc. It is not possible to group the presentations under identifiable topic areas and the contents have therefore been organized in sections devoted to the invited lectures and the contributed papers. Within the contributed papers there are two small subsections devoted to (a) industrial design and (b) mathematical education for industry. In each section papers are listed in alphabetical order by name of first author.

Numerical Analysis is an interdisciplinary topic which develops its strength only when viewed in close connection with applications. Nowadays, mechanical engineers having computer simulation as a daily engineering tool have to learn more and more techniques from that field. Mathematicians, on the other hand, are increasingly confronted with the need for developing special purpose methods and codes. This requires a broad interdisciplinary understanding and a sense for model-method interactions. With this monograph we give an introduction to selected topics of Numerical Anal­ ysis based on these facts. We dedicate our presentations to an interesting discipline in computational engineering: multibody dynamics. Though the basic ideas and methods apply to other engineering fields too, we emphasize on having one homo­ geneous class of applications. Both authors worked through many years in teams developing multibody codes. Interdisciplinary work also includes transferring ideas from one field to the other and a big amount of teaching -and that was the idea of this book. This book is intended for students of mathematics, engineering and computer sci­ ence, as well as for people already concerned with the solution of related topics in university and industry. After a short introduction to multibody systems and the mathematical formulation of the equations of motion, different numerical methods used to solve simulation tasks are presented. The presentation is supported by a simple model of a truck. This truck model will follow the reader from the title page to the appendix in various versions, specially adapted to the topics.

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June 20-25, 1987, ISI Torino