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Partielle Differentialgleichungen by Peter Meinhold, Eberhard Wagner

Partielle Differentialgleichungen

by Peter Meinhold , Eberhard Wagner
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Book cover type: Paperback
  • ISBN13: 9783322002570
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 117
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 6. Aufl. 1975
  • Item Weight: 205 grams
  • BISAC Subject(s): Engineering (General)

Die mathematische ModelIierung deterministischer Prozesse aus Physik und Tech- nik, aber auch aus anderen Wissenschaftsgebieten, führt sehr häufig auf Differential- gleichungen. Der Grund hierfür liegt letztlich darin, da oftmals die "Triebkräfte des Prozesses" durch räumliche und/oder zeitliche Änderungen der gesuchten Funk- tionen beschrieben werden (man denke etwa als einfaches Beispiel an das Newtonsche Grundgesetz) und da dadurch Ableitungen dieser Funktionen mit auftreten. Handelt es sich.. dabei um eine Differentialgleichung für eine Funktion von mehreren Ver- änderlichen, so spricht man von einer partiellen Differentialgleichung. Das Gebiet der partiellen Differentialgleichungen ist au erordentlich umfangreich und erfordert für tiefere Untersuchungen Methoden, die weit über das Anliegen dieser Lehrbuchreihe hinausreichen. Dieser Band kann deshalb dem Leser nur einen einführenden Einblick in einige typische AufgabensteIlungen und Lösungsmethoden geben und damit einen Ausgangspunkt für weitere Literaturstudien schaffen. Auf Systeme von partiellen Differentialgleichungen mu te völlig verzichtet werden. Die partiellen Differentialgleichungen I. Ordnung werden im Kapitel 2 behandelt. Ihre Theorie ist gut ausgebaut. Ein wichtiges Ergebnis ist dabei - auch für nicht- lineare Gleichungen - die Rückführbarkeit auf gewöhnliche Differentialgleichungs- systeme. Von besonderer Bedeutung sind in den Anwendungen Differentialgleichungen 2. Ordnung. Ihre Vielfalt und ihr unterschiedliches Verhalten erfordern sowohl aus theoretischer als auch aus praktischer Sicht eine weitere Klassifikation. Diese Klassi- fikation wird im Kapitel 3 für gewisse fastlineare Gleichungen 2. Ordnung durch- geführt. Es folgen einige elementare Lösungsmethoden für lineare Gleichungen 2. Ordnung auf der Grundlage des Superpositionsprinzips.

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