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Partial Differential Equations: An Introduction to Analytical and Numerical Methods - Couverture souple
Synopsis
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach.
A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension.
Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Wolfgang Arendt is Senior Professor of Analysis at Ulm University. His research areas are functional analysis and partial differential equations.
Karsten Urban is Professor of Numerical Mathematics at Ulm University. His research interests include numerical methods for partial differential equations, especially with concrete applications in science and technology.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Partial Differential Equations
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Intertwines analytical and numerical methods for an integrated approachShowcases examples from the physical sciences, engineering, and economicsIncludes numerous exercises, illustrations, and opportunities for extensionWolfgan. N° de réf. du vendeur 1289955108
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Partial Differential Equations: An Introduction to Analytical and Numerical Methods: 294 (Graduate Texts in Mathematics)
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Partial Differential Equations : An Introduction to Analytical and Numerical Methods
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Springer International Publishing, 2024
ISBN 10 : 3031133811
ISBN 13 : 9783031133817
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach.A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple(TM) completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension.Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed. N° de réf. du vendeur 9783031133817
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Partial Differential Equations: An Introduction to Analytical and Numerical Methods (Graduate Texts in Mathematics)
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Partial Differential Equations
ISBN 10 : 3031133811
ISBN 13 : 9783031133817
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Taschenbuch. Etat : Neu. Neuware -This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach.A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple¿ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson¿s equation, the heat equation, and the wave equation on Euclidean domains. The Black¿Scholes equation from mathematical finance is one of several opportunities for extension.Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 476 pp. Englisch. N° de réf. du vendeur 9783031133817
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Partial Differential Equations: An Introduction to Analytical and Numerical Methods (Paperback or Softback)
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