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The purpose of the book is a dual one: to detail the nature and
results of Tunguska investigations in the former USSR and
present-day CIS, and to destroy two long-standing myths still held
in the West. The first concerns alleged "final solutions" that have
ostensibly been found in Russia or elsewhere. The second concerns
the mistaken belief that there has been little or no progress in
understanding the nature of the Tunguska phenomenon. All this is
treated by the author in a scholarly and responsible manner.
Although the book does present certain unusual findings of Russian
and Ukrainian scholars, it is important to stress that this is not
a sensational book; it is, rather, a serious exposition of the
results of rational investigations into a difficult scientific
problem. We are demonstrating the true complexity of the problem
that is now entering its second century of existence. Simple
meteoritic models cannot explain all the characteristics of this
complicated event, and therefore certain so-called "unconventional
hypotheses" about the nature of the Tunguska explosion are to be
considered as well.
Methods from contact and symplectic geometry can be used to solve
highly non-trivial nonlinear partial and ordinary differential
equations without resorting to approximate numerical methods or
algebraic computing software. This book explains how it's done. It
combines the clarity and accessibility of an advanced textbook with
the completeness of an encyclopedia. The basic ideas that Lie and
Cartan developed at the end of the nineteenth century to transform
solving a differential equation into a problem in geometry or
algebra are here reworked in a novel and modern way. Differential
equations are considered as a part of contact and symplectic
geometry, so that all the machinery of Hodge-deRham calculus can be
applied. In this way a wide class of equations can be tackled,
including quasi-linear equations and Monge-Ampere equations (which
play an important role in modern theoretical physics and
meteorology).
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