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Interpolation und Modellierung von Kurven und Flächen by Vaupel, Jürgen

Interpolation und Modellierung von Kurven und Flächen

by Jürgen Vaupel
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Book cover type: Paperback
  • ISBN13: 9783346586261
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 76
  • Original Price: USD 34.9
  • Language: German
  • Edition: N/A
  • Item Weight: 109 grams
  • BISAC Subject(s): Schools / Levels / Secondary

Zusammenfassung aus dem Jahr 2022 im Fachbereich Lernmaterialien - Mathematik, Sprache: Deutsch, Abstract: Die Interpolation von numerischen Daten zu einer Funktion ist eine klassische Aufgabe der numerischen Mathematik und wird in ihren Grundlagen bereits in der Schule behandelt. Für die Lösung solcher Interpolationsaufgaben gibt es Standardverfahren, die bereits auf elementarem Niveau verdeutlichen, dass eine geschickte Wahl des Lösungsansatzes eine erhebliche Reduktion des Rechenaufwandes zur Folge haben kann. Im ersten Kapitel werden die Interpolationsverfahren von Newton, Lagrange und Hermite überblickartig vorgestellt sowie die zugehörigen Quadraturformeln entwickelt. Der Fokus des zweiten Kapitels liegt auf der Approximation von Funktionen durch Polynome. Gegenstand des dritten Kapitels sind die Theorie und die Praxis der Interpolation mit Splinefunktionen, insbesondere mit natürlichen kubischen Splines, welche eine bemerkenswerte Minimaleigenschaft besitzen. Von einfachen "Steckbriefaufgaben" aus dem Mathematikunterricht der Oberstufe bis zu den NURBS-Flächen: so lässt sich die inhaltliche Spannweite dieses Textes beschreiben, der sich an Lehrerinnen und Lehrer, mathematisch interessierte Oberstufenschülerinnen und -schüler, aber auch an Studierende der MINT-Fächer wendet.

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