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Partielle Differenzialgleichungen

Partielle Differenzialgleichungen


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About the Book

1 Modellierung, oder wie man auf eine Differenzialgleichung kommt 1.1 Modellierung mit Differenzialgleichungen 1.2 Transport-Prozesse 1.3 Diffusion 1.4 Die Wellengleichung 1.5 Die Black-Scholes-Gleichung 1.6 Jetzt wird es mehrdimensional 1.7 Es gibt noch mehr 1.8 Klassifikation partieller Differenzialgleichungen 1.9 Aufgaben 2 Kategorisierung und Charakteristiken 2.1 Charakteristiken von Anfangswertproblemen auf R 2.2 Gleichungen zweiter Ordnung 2.3 Anfangs- und Randwerte 2.4 Nichtlineare Gleichungen zweiter Ordnung 2.5 Gleichungen höherer Ordnung und Systeme 2.6 Aufgaben 3 Elementare Lösungsmethoden 3.1 Variablentransformation für die Transportgleichung 3.2 Trennung der Variablen am Beispiel der Wellengleichung 3.3 Fourier-Reihen 3.4 Die Laplace-Gleichung 3.5 Die Wärmeleitungsgleichung 3.6 Die Black-Scholes-Gleichung 3.7 Integral-Transformationen 3.8 Aufgaben 4 Hilbert-Räume 4.1 Unitäre Räume 4.2 Orthonormalbasen 4.3 Vollständigkeit 4.4 Orthogonale Projektionen 4.5 Linearformen und Bilinearformen 4.6 Schwache Konvergenz 4.7 Stetige und kompakte Operatoren 4.8 Der Spektralsatz 4.9 Aufgaben 5 Sobolev-Räume und Randwertaufgaben in einer Dimension 5.1 Sobolev-Räume in einer Variablen 5.2 Randwertprobleme auf einem Intervall 5.3 Aufgaben 6 Sobolev-Räume und Hilbert-Raum-Methoden für elliptische Gleichungen 6.1 Regularisierung 6.2 Sobolev-Räume 6.3 Der Raum H1 6.4 Die Poisson-Gleichung mit Dirichlet-Randbedingungen 6.5 Sobolev-Räume und Fourier-Transformation 6.6 LokaleRegularität 6.7 Die Poisson-Gleichung mit inhomogenen Dirichlet-Randbedingungen 6.8 Das Dirichlet-Problem 6.9 Elliptische Gleichungen mit Dirichlet-Randbedingung 6.10 H2-Regularität 6.11 Kommentare zu Kapitel 6 6.12 Aufgaben 7 Elliptische Gleichungen mit Neumann- und Robin-Randbedingungen 7.1 Der Satz von Gauß 7.2 Beweis des Satzes von Gauß 7.3 Die Fortsetzungseigenschaft 7.4 Die Poisson-Gleichung mit Neumann-Randbedingungen 7.5 Der Spursatz und Robin-Randbedingungen 7.6 Kommentare zu Kapitel 7 7.7 Aufgaben 8 Spektralzerlegung und Evolutionsgleichungen 8.1 Ein vektorwertiges Anfangswertproblem 8.2 Die Wärmeleitungsgleichung mit Dirichlet-Randbedingungen 8.3 Die Wärmeleitungsgleichung mit Robin-Randbedingungen 8.4 Die Wellengleichung 8.5 Aufgaben 9 Numerische Verfahren 9.1 Finite Differenzen 9.2 Finite Elemente 9.3 Ergänzungen und Erweiterungen 9.4 Parabolische Probleme 9.5 Aufgaben 10 Maple, oder manchmal hilft der Computer 10.1 Maple(R) 10.2 Aufgaben
About the Author:

Wolfgang Arendt ist Seniorprofessor für Analysis an der Universität Ulm. Sein Forschungsgebiet sind Funktionalanalysis und Partielle Differenzialgleichungen.

Karsten Urban ist Professor für Numerische Mathematik an der Universität Ulm. Er forscht u.a. auf dem Gebiet der numerischen Verfahren für partielle Differenzialgleichungen, insbesondere mit konkreten Anwendungen in Naturwissenschaft und Technik.


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Product Details
  • ISBN-13: 9783662583210
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Height: 244 mm
  • No of Pages: 407
  • Spine Width: 22 mm
  • Weight: 720 gr
  • ISBN-10: 3662583216
  • Publisher Date: 24 Jan 2019
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Sub Title: Eine Einführung in Analytische Und Numerische Methoden
  • Width: 170 mm


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