000			04346nam a22005175i 4500
001			978-0-387-25265-0
003			DE-He213
005			20161121231012.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387252650 _9978-0-387-25265-0
024	7		_a10.1007/b107051 _2doi
050		4	_aTA329-348
050		4	_aTA640-643
072		7	_aTBJ _2bicssc
072		7	_aMAT003000 _2bisacsh
082	0	4	_a519 _223
100	1		_aMeleshko, S. V. _eauthor.
245	1	0	_aMethods for Constructing Exact Solutions of Partial Differential Equations _h[electronic resource] : _bMathematical and Analytical Techniques with Applications to Engineering / _cby S. V. Meleshko.
264		1	_aBoston, MA : _bSpringer US, _c2005.
300			_aXVI, 352 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aEquations with One Dependent Function -- Systems of Equations -- Method of the Degenerate Hodograph -- Method of Differential Constraints -- Invariant and Partially Invariant Solutions -- Symmetries of Equations with Nonlocal Operators -- Symbolic Computer Calculations.
520			_aDifferential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each solution of a system of differential equations corresponds to a particular process. Therefore, methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations. The emphasis is on the methods of differential constraints, degenerate hodograph and group analysis. These methods have become a necessary part of applied mathematics and mathematical physics. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. The description of algorithms contains illustrative examples which are typically taken from continuum mechanics. Some sections of the book introduce new applications and extensions of these methods, such as integro-differential and functional differential equations, a new area of group analysis. It should also be noted that the method of differential constraints is not well known outside Russia; there are only a few books in English where the idea behind this method (without analysis) is briefly mentioned. This book is a result of an effort to introduce, at a fairly elementary level, many methods for constructing exact solutions collected in one book. It is based on the author's research and various courses and lectures given to undergraduate and graduate students, as well as professional audiences over the past twenty-five years. The book is assembled, in a coherent and comprehensive way, from results that are scattered across many different articles and books published over the last thirty years. The approach is analytical. Introductions to theories are followed by examples. The book is written for students, engineers and scientists with diverse backgrounds and interests. For a deeper coverage of a particular method or an application, the readers are referred to special-purpose books and/or scientific articles referenced in the book. The prerequisites for the study are standard courses in calculus, linear algebra, and ordinary and partial differential equations.
650		0	_aEngineering.
650		0	_aDifferential equations.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650		0	_aPhysics.
650		0	_aFluid mechanics.
650	1	4	_aEngineering.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
650	2	4	_aApplications of Mathematics.
650	2	4	_aTheoretical, Mathematical and Computational Physics.
650	2	4	_aEngineering Fluid Dynamics.
650	2	4	_aOrdinary Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387250601
856	4	0	_uhttp://dx.doi.org/10.1007/b107051
912			_aZDB-2-ENG
950			_aEngineering (Springer-11647)
999			_c507114 _d507114