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Einführung in die Theorie der Differentialgleichungen im Reellen Gebiet: (83 Grundlehren der mathematischen Wissenschaften)

Einführung in die Theorie der Differentialgleichungen im Reellen Gebiet: (83 Grundlehren der mathematischen Wissenschaften)

          
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About the Book

Wie der Titel sagt, will dies Buch in die Lehre von den Differential­ gleichungen einführen. In der Theorie spielt die Auffindung geschlos­ sener Ausdrücke für die Integrale eine geringe Rolle, denn meist kann man die Eigenschaften dfr Lösungen leichter an der Differential­ gleichung selbst als an expliziten Ausdrücken ablesen. Die Untersuchung der Natur der Lösungen ist aber die Aufgabe der Theorie. Dement­ sprechend gebe ich schon in der Einleitung im einfachsten Fall einer gewöhnlichen Differentialgleichung dy dx = j(x, y) Existenz- und Unitätssatz unter der Annahme einer LIPSCHITZ­ Bedingung für j (x, y). So geht der Leser schon mit einem gewissen Kenntnisstand über Differentialgleichungen an die systematische Dar­ stellung heran, die mit § 1 anhebt. Dieser Abschnitt klärt Existenz­ probleme und Fragen über die Gesamtheit aller Lösungen für alle gewöhnlichen Differentialgleichungen, bei denen die Ableitungen stetig von der unabhängigen Variablen und den unbekannten Funktionen abhängen. § 1 ist sehr ausführlich gehalten, da er die Grundlage alles Weiteren ist. Der § 2 wendet die gewonnenen Einsichten auf einige wichtige Typen von Differentialgleichungen an. Der § 3 ist einer ein­ dringlichen Darstellung der stationären Differentialgleichungen ge­ widmet, bei denen die Ableitungen nur von den unbekannten Funk­ tionen abhängen. Daran anschließend ergibt sich auch einiges bei Differentialgleichungen, deren stationärer Charakter durch den Zutritt relativ kleiner auch von der unabhängigen Veränderlichen abhängiger Glieder gestört ist.

Table of Contents:
§ 0. Einleitung.- § 1. Existenzsätze für gewöhnliche Differentialgleichungen.- § 2. Berechnung der Lösungen.- § 3. Stationäre und nahezu stationäre Differentialgleichungen.- § 4. Randwertaufgaben.- § 5. Partielle Differentialgleichungen erster Ordnung.- Namen- und Sachverzeichnis.


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Product Details
  • ISBN-13: 9783642672279
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Edition: Softcover Reprint of the Origi ed.
  • Language: German
  • Returnable: N
  • Series Title: 83 Grundlehren der mathematischen Wissenschaften
  • Weight: 417 gr
  • ISBN-10: 3642672272
  • Publisher Date: 10 Nov 2013
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 281
  • Returnable: Y
  • Spine Width: 16 mm
  • Width: 155 mm


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Einführung in die Theorie der Differentialgleichungen im Reellen Gebiet: (83 Grundlehren der mathematischen Wissenschaften)
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Einführung in die Theorie der Differentialgleichungen im Reellen Gebiet: (83 Grundlehren der mathematischen Wissenschaften)
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