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.

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.

'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."