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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Partial Differential Equations
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Partial Differential Equations
Wolfgang Arendt, Karsten Urban (Broschiert, Englisch)
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Beschreibung
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. 53,49 €
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Technische Daten
Erscheinungsdatum
03.01.2024
Sprache
Englisch
EAN
9783031133817
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Wolfgang Arendt, Karsten Urban
Seitenanzahl
452
Auflage
1
Einbandart
Broschiert
Hersteller: Springer Nature Customer Service Center GmbH, ProductSafety@springernature.com
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