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001			95913
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006			m o d
007			cr cnu|||unuuu
008			170502s2017 sz a ob 001 0 eng d
020			_a3319552120 _q(electronic bk.)
020			_a9783319552125 _q(electronic bk.)
020			_z3319552112
020			_z9783319552118 _q(print)
040			_aN$T _cN$T _dGW5XE _dEBLCP _dYDX _dN$T _dAZU _dUPM _dOCLCF _dUAB _dESU _dIOG _dCOO _dVT2 _dMERER _dOCLCQ _dU3W _dES-MaUEC _bspa
050		4	_aQA377 _b.E678 2017 EB
100	1		_aEpstein, M. _q(Marcelo), _eautor
245	1	0	_aPartial differential equations : _bmathematical techniques for engineers _cMarcelo Epstein.
264		1	_aCham, Switzerland _bSpringer _c2017.
300			_a1 recurso en línea (xiii, 255 páginas) _bilustraciones (algunas a color)
336			_aTexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aMathematical engineering _x2192-4732
500			_aSpringerLink _bSpringer Engineering eBooks 2017 English+International
504			_aIncluye referencias bibliográficas e índice
505	0		_aPreface; Contents; Part I Background; 1 Vector Fields and Ordinary Differential Equations; 1.1 Introduction; 1.2 Curves and Surfaces in mathbbRn; 1.2.1 Cartesian Products, Affine Spaces; 1.2.2 Curves in mathbbRn; 1.2.3 Surfaces in mathbbR3; 1.3 The Divergence Theorem; 1.3.1 The Divergence of a Vector Field; 1.3.2 The Flux of a Vector Field over an Orientable Surface; 1.3.3 Statement of the Theorem; 1.3.4 A Particular Case; 1.4 Ordinary Differential Equations; 1.4.1 Vector Fields as Differential Equations; 1.4.2 Geometry Versus Analysis; 1.4.3 An Example.
505	8		_a1.4.4 Autonomous and Non-autonomous Systems1.4.5 Higher-Order Equations; 1.4.6 First Integrals and Conserved Quantities; 1.4.7 Existence and Uniqueness; 1.4.8 Food for Thought; References; 2 Partial Differential Equations in Engineering; 2.1 Introduction; 2.2 What is a Partial Differential Equation?; 2.3 Balance Laws; 2.3.1 The Generic Balance Equation; 2.3.2 The Case of Only One Spatial Dimension; 2.3.3 The Need for Constitutive Laws; 2.4 Examples of PDEs in Engineering; 2.4.1 Traffic Flow; 2.4.2 Diffusion; 2.4.3 Longitudinal Waves in an Elastic Bar; 2.4.4 Solitons.
505	8		_a2.4.5 Time-Independent Phenomena2.4.6 Continuum Mechanics; References; Part II The First-Order Equation; 3 The Single First-Order Quasi-linear PDE; 3.1 Introduction; 3.2 Quasi-linear Equation in Two Independent Variables; 3.3 Building Solutions from Characteristics; 3.3.1 A Fundamental Lemma; 3.3.2 Corollaries of the Fundamental Lemma; 3.3.3 The Cauchy Problem; 3.3.4 What Else Can Go Wrong?; 3.4 Particular Cases and Examples; 3.4.1 Homogeneous Linear Equation; 3.4.2 Non-homogeneous Linear Equation; 3.4.3 Quasi-linear Equation; 3.5 A Computer Program; References; 4 Shock Waves; 4.1 The Way Out.
505	8		_a4.2 Generalized Solutions4.3 A Detailed Example; 4.4 Discontinuous Initial Conditions; 4.4.1 Shock Waves; 4.4.2 Rarefaction Waves; References; 5 The Genuinely Nonlinear First-Order Equation; 5.1 Introduction; 5.2 The Monge Cone Field; 5.3 The Characteristic Directions; 5.4 Recapitulation; 5.5 The Cauchy Problem; 5.6 An Example; 5.7 More Than Two Independent Variables; 5.7.1 Quasi-linear Equations; 5.7.2 Non-linear Equations; 5.8 Application to Hamiltonian Systems; 5.8.1 Hamiltonian Systems; 5.8.2 Reduced Form of a First-Order PDE; 5.8.3 The Hamilton -- Jacobi Equation; 5.8.4 An Example.
520	3		_aThis monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.
650		7	_aEcuaciones diferenciales _2embne _0(OCoLC)fst00893484 _0 _9139227
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=http://link.springer.com/10.1007/978-3-319-55212-5 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
988			_aEBOOK, asignarmaterias, EBSPRINGER_2017C
998			_b02/2018 _dz _e- _zSI
999			_c95913 _d95913 _x1