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Record Nr. |
UNINA9910637713003321 |
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Autore |
Arendt Wolfgang <1950-> |
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Titolo |
Partial differential equations : an introduction to analytical and numerical methods / / Wolfgang Arendt, Karsten Urban ; translated by James B. Kennedy |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2023] |
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©2023 |
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ISBN |
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Descrizione fisica |
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1 online resource (463 pages) |
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Collana |
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Graduate texts in mathematics ; ; 294 |
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Disciplina |
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Soggetti |
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Differential equations, Partial |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Foreword by the Translator -- Preface -- Acknowledgments -- About the Authors -- About the Translator -- Contents -- List of figures -- 1 Modeling, or where do differential equations come from -- 1.1 Mathematical modeling -- 1.1.1 Modeling with partial differential equations -- 1.1.2 Modeling is only the first step -- 1.2 Transport processes -- 1.2.1 Conservation laws -- 1.2.2 From a conservation law to a differential equation -- 1.2.3 The linear transport equation -- 1.2.4 The convection-reaction equation -- 1.2.5* Burgers' equation -- 1.3 Diffusion -- 1.4 The wave equation -- 1.5 The Black-Scholes equation -- 1.6 Let's get higher dimensional -- 1.6.1 Transport processes -- 1.6.2 Diffusion processes -- 1.6.3 The wave equation -- 1.6.4 Laplace's equation -- 1.7* But there's more -- 1.7.1 The KdV equation -- 1.7.2 Geometric differential equations -- 1.7.3 The plate equation -- 1.7.4 The Navier-Stokes equations -- 1.7.5 Maxwell's equations -- 1.7.6 The Schrödinger equation -- 1.8 Classification of partial differential equations -- 1.9* Comments -- 1.10 Exercises -- 2 Classification and characteristics -- 2.1 Characteristics of initial value problems on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 2.1.1 Homogeneous problems -- 2.1.2 Inhomogeneous problems -- 2.1.3* Burgers' equation -- 2.2 Equations of second order -- 2.3* Nonlinear equations of second order |
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