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020 _a9783319020990
_9978-3-319-02099-0
024 7 _a10.1007/978-3-319-02099-0
_2doi
035 _ato000542218
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aOlver, Peter J.
_eauthor.
_9322376
245 1 0 _aIntroduction to Partial Differential Equations
_helectronic resource
_cby Peter J. Olver.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXXV, 635 p. 143 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aUndergraduate Texts in Mathematics,
_x0172-6056
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.   .
650 0 _amathematics.
_9566183
650 0 _aFourier analysis.
_9566348
650 0 _aDifferential equations, partial.
_9303599
650 1 4 _aMathematics.
_9566184
650 2 4 _aPartial Differential Equations.
_9303602
650 2 4 _aComplex Systems.
_9412218
650 2 4 _aFourier Analysis.
_9566349
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aUndergraduate Texts in Mathematics,
_9306113
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02099-0
912 _aZDB-2-SMA
999 _c399882