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'Bt moi ..... si j'avait 50 comment en revenir. je One service
IlUllbcmatics has rendered the human race. It has put common sense
back n'y ser.lis point a116.' IulesVeme where it belongs. on the
topmost shelf next to the dusty canister labelled 'discarded
IIOIISCIISC.. Erie T. Bell The series is divergent; thelefore we
may be able to do something with it. O. Heaviside Mathematics is a
tool for thought. A highly necessary tool in a world where both
feedback and nonlineari ties abound. Similarly. all kinds of parts
of mathematics serve as tools for other parts and for other sci
ences. Applying a simple rewriting rule to the quote on the right
above one finds such statements as: 'One ser vice topology has
rendered mathematical physics ....; 'One service logic has rendered
computer science .. .'; 'One service category theory has rendered
mathematics .. .'. All arguably true. And all statements obtainable
this way form part of the raison d'8tre of this series."
This book has come into being as a result ofthe author's lectures
on mathematical modelling rendered to the students, BS and MS
degree holders specializing in applied mathematics and computer
science and to post-graduate students in exact sciences of the
Nizhny Novgorod State University after N. . Lobatchevsky. These
lectures are adapted and presented as a single whole ab out
mathematical models and modelling. This new course of lectures
appeared because the contemporary Russian educational system in
applied mathematics rested upon a combination of fundamental and
applied mathematics training; this way of training oriented
students upon solving only the exactly stated mathematical
problems, and thus there was created a certain estrangement to the
most essential stages and sides of real solutions for applied
problems, such as thinking over and deeply piercing the essence of
a specific problem and its mathematical statement. This statement
embraces simplifications, adopted idealizations and creating a
mathematical model, its correction and matching the results
obtained against a real system. There also existed another main
objective, namely to orient university graduates in their future
research not only upon purely mathematical issues but also upon
comprehending and widely applying mathematics as a universal
language of contemporary exact science, and mathematical modelling
as a powerful me ans for studying nature, engineering and human
society.
This book helps the reader become familiar with various mathematical models for mechanical, electrical, physical, atronomical, chemical, biological, ecological, cybernetical and other systems and processes. The models examined are evolutionary models, i.e. the models of time-varying processes known as dynamic systems, such as fluid flow, biological processes, oscillations in mechanical and electromagnetic systems, and social systems. The book shows readers how to identify appropriate situations for modelling, how to address difficulties in creating models, and how to learn what mathematics teaches us about the modelling of dynamical phenomena in our surrounding world. It is interesting for a wide spectrum of readers, students of natural science and engineering, and also for researchers in these fields.
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