Numerische Mathematik Für Informatiker
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Dieses Buch ist aus einem Fernstudienkurs entstanden, den ich seit dem Winterse- mester 1989/90 in jährlichem Rhythmus den Studenten der FernUniversität Ha- gen im Diplomstudiengang Informatik als dritten Teil eines viersemestrigen Zy- klus "Mathematik für Informatiker I-IV" anbiete. Form, Aufbau und Inhalt die- ses Buches lassen seine Genesis erkennen; es ist in manchem anders als die mei- sten Lehrbücher über Numerik: Ein Fernstudienkurs mu selbstinstruierend sein, so da der Lehrstoff etwas breiter als üblich dargestellt ist. Insbesondere sind viele Beispiele und Aufgaben, die teilweise auch Beweise vervollständigen, mit knappen Lösungshinweisen aufgeführt. Auch die zahlreichen Abbildungen und Tabellen un- terstreichen den selbstinstruierenden Charakter dieses Buches. Ein Fernstudienkurs sollte, was den dargebotenen Lehrstoff anbelangt, weitgehend autark sein und nur die Anfängervorlesungen als Grundlage voraussetzen. Der Leser findet deshalb an einigen Stellen kurze" Ausflüge" in andere Gebiete der Mathematik, mit denen die Numerik fundiert wird, die aber andernorts verzichtbar sind, da sie den Studen- ten bei einem breiteren Mathematikangebot bereits vertraut sein mü ten. Zentrale Begriffsbildungen müssen ohnedies von der konstruktiven Seite beleuchtet werden, auch wenn sie schon unter "reinen Aspekten" (Axiomatik, Existenz, Eindeutigkeit) behandelt wurden. Schlie lich sollte die Stoffauswahl "Klassik" und "Moderne", grundlegende numerische Verfahren und aktuelle, computerbezogene Algorithmen verbinden. Der Nachdruck liegt dabei auf der Nähe zur Informatik: Gro en Raum nehmen die mathematischen Grundlagen von Kurven-und Flächendarstellungen mit Hilfe von Splines, die Behandlung von periodischen Vorgängen mittels FFT sowie die speziellen Techniken für gro e, schwach besetzte lineare Gleichungssysteme ein.
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