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008			231113s2020 gw a|||fr |||1 0|eng c
010			_a 2019740195
020			_a9783319020990
040			_aDIBRA _beng _erda _cUVAL
041	0		_aeng
082	0	4	_a515.353 _223
100	1		_aOlver, Peter J., _eautor. _9241001.
245	1	0	_aIntroduction to partial differential equations / _cby Peter J. Olver.
250			_aFirst edition 2014.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c[2020]
264		4	_c©2020
300			_axxv, 636 páginas : _bilustraciones.
347			_2rda _atext file _bPDF
490	0		_aUndergraduate Texts in Mathematics, _x0172-6056
500			_aIncluye índice.
505	0		_aWhat are Partial Differential Equations? -- Linear and Nonlinear Waves -- Fourier Series -- Separation of Variables -- Finite Differences -- Generalized Functions and Green's Functions -- Complex Analysis and Conformal Mapping -- Fourier Transforms -- Linear and Nonlinear Evolution Equations -- A General Framework for Linear Partial Differential Equations -- Finite Elements and Weak Solutions -- Dynamics of Planar Media -- Partial Differential Equations in Space .
520			_aThis textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests are centered on the development of symmetry-based methods for differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research journals as well as 4 other books, including the definitive Springer graduate text, Applications of Lie Groups to Differential Equations, and another undergraduate text, Applied Linear Algebra. A Solutions Manual for instrucors is available by clicking on "Selected Solutions Manual" under the Additional Information section on the right-hand side of this page.
588			_aDescription based on publisher-supplied MARC data.
650	1	4	_aECUACIONES DIFERENCIALES PARCIALES _96940.
650	1	4	_aTEORIA DE SISTEMAS _9233798.
650	1	4	_aANALISIS DE FOURIER _96916.
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056.
942			_2ddc _cBK
999			_c288393 _d288393