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Auteur Peter J. Olver |
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Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : Peter J. Olver, Auteur Editeur : Springer International Publishing Année de publication : 2014 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-02099-0 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique
[Termes IGN] équation de Laplace
[Termes IGN] équation de Poisson
[Termes IGN] équation différentielle
[Termes IGN] équation linéaire
[Termes IGN] équation non linéaire
[Termes IGN] équation polynomiale
[Termes IGN] fonction de Green
[Termes IGN] principe de Huygens
[Termes IGN] transformation de Fourier
[Termes IGN] valeur limiteRésumé : (auteur) This 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.Note de contenu : 1- What Are Partial Differential Equations?
2- Linear and Nonlinear Waves
3- Fourier Series
4- Separation of Variables
5- Finite Differences
6- Generalized Functions and Green’s Functions
7- Fourier Transforms
8- Linear and Nonlinear Evolution Equations
9- A General Framework for Linear Partial Differential Equations
10- Finite Elements and Weak Solutions
11- Dynamics of Planar Media
12- Partial Differential Equations in SpaceNuméro de notice : 25874 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-02099-0 En ligne : https://doi.org/10.1007/978-3-319-02099-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95568