000			02624nam a22002057a 4500
003			OSt
005			20220927163445.0
008			220927b |||||||| |||| 00| 0 eng d
020			_a9783319020983
040			_cICTS
050			_aQA377
100			_aOlver, Peter J.
245			_aIntroduction to partial differential equations
260			_aSwitzerland _bSpringer _c2014
300			_axxv, 635 pp.
505			_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 cover 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
650			_aMathematics; Differential equations; Partial differential equations
942			_2lcc _cBK
999			_c3189 _d3189