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Differentialgeometrie: Kurven Und Flächen by Volkmar Wünsch

Differentialgeometrie: Kurven Und Flächen

by Volkmar Wünsch
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Book cover type: Paperback
  • ISBN13: 9783815420959
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 208
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 1997
  • Item Weight: 345 grams
  • BISAC Subject(s): Applied

Die Geschichte der Differentialgeometrie ist eng mit der Entwicklung der Infini- tesimalrechnung und der analytischen Geometrie einerseits, mit der Geodäsie, der Kartographie und der Physik andererseits verknüpft. Sie ist zwar durch Idealisierung der Erfahrungswelt entstanden, hat sich aber im Laufe der letzten beiden Jahrhunderte zu einer deduktiven, mit strengen Beweisen arbeitenden Wissenschaft herausgebildet. Heute sind zahlreiche Disziplinen der Mathema- tik, aber auch der Physik und Technik mit differentialgeometrischen Begriffs- bildungen durchsetzt. Diese interdisziplinäre Verzahnung -man denke etwa an die Darstellung geometrischer Objekte mit den Methoden der Numerik und Informatik (CAGD) oder an die Geometrisierung der modernen Physik -hält unvermindert an. Mit dem vorliegenden Buch wird einem möglichst gro en Interessentenkreis eine brauchbare Grundlage für eine klassisch-und anwendungsorientierte Kurven- und Flächentheorie geliefert. In der Differentialgeometrie kann ein Studieren- der die in der Differential- und Integralrechnung sowie in der analytischen Geometrie erworbenen Techniken anwenden und geometrische Vorstellungen entwickeln. Dem Leser sollen Brücken zwischen Theorie und Praxis aufgezeigt werden. Im Vordergrund stehen die lokale Differentialgeometrie und ihre An- wendungsmöglichkeiten, wobei lokale und globale Aspekte klar unterschieden werden. Gelegentlich wird dem technisch Wichtigen der Vorrang vor dem geo- metrisch Wertvollen eingeräumt. Gleichwohl sollen die technischen Anwendun- gen nicht von den geometrischen Grundgedanken ablenken. Differentialgeo- metrie wird eben nicht nur als Grundlage technischer Bildung, sondern auch wegen ihres Stellenwertes im Rahmen der Mathematik und ihrer kulturellen Bedeutung betrieben.

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