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Integralgleichungen by Wolfgang Hackbusch

Integralgleichungen

by Wolfgang Hackbusch
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Book cover type: Paperback
  • ISBN13: 9783519023708
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 375
  • Original Price: GBP 39.99
  • Language: German
  • Edition: 1989
  • Item Weight: 440 grams
  • BISAC Subject(s): Calculus

Die Integralgleichungen stellen ein Gebiet dar. das f�r sich durchaus selbst�ndig ist und auf einer interessanten Mischung von Analysis. Funktionentheorie und Funktionalanalysis beruht. Auf der anderen Seite gewinnen die Integralgleichungen ihr praktisches Interesse aus der Integralgleichungsmethode . die es erlaubt, partielle Differential- gleichungen in Integralgleichungen umzuformen. Das Buch ist aus Vorlesungen hervorgegangen, die der Autor an der Ruhr-Universit�t Bochum und der Christian-Albrechts-Universit�t Kiel gehalten hat. Der Umfang der Kapitel 1 bis 6 entspricht etwa einer intensiven vierst�ndigen Vorlesung. Das Studium der Integral- gleichungen kann mit Vorkenntnissen der Analysis und den Grundlagen der Numerik aufgenommen werden. Kenntnisse aus der Funktional- analysis sind hilfreich. aber nicht unabdingbar, wenn Grundbegriffe wie Banach-und Hilbert-R�ume gel�ufig sind. Der Theorieteil dieses Buches ist so knapp wie m�glich bemessen. da die Numerik in den Kapiteln 2. 4, 5 im Vordergrund stehen soll. Wichtige Teile der ben�tigten Funktionalanalysis wie etwa die Riesz-Schauder-Theorie werden ohne Herleitung wiedergegeben. Es wird dabei davon ausgegangen. da dem Leser dieses Gebiet entweder aus einer Vorlesung �ber Funktionalanalysis bekannt ist oder da e- mit gesteigerter Motivation durch praktische Beispiele - diese Kapitel durch Vorlesungen oder Lekt�re nachholen wird. Es sei daran erinnert. da auch historisch die Funktionalanalysis aus der Diskussion der Integralgleichungen hervorgegangen ist. Als Funktionenr�ume werden in dieser Darstellung vornehmlich die klassischen der stetigen oder H�lder-stetigen Funktionen verwendet. Die Sobolev-R�ume werden weitgehend vermieden. was zum Beispiel zur Folge hat. da dieIntegraloperatoren hier nicht in der erforderlichen Allgemeinheit als Pseudodifferentialoperatoren diskutiert werden k�nnen.

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