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Komplexe Zahlen und ebene Geometrie

Komplexe Zahlen und ebene Geometrie


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About the Book

Komplexe Zahlen sind ein wichtiges Darstellungsmittel für zentrale Problemstellungen der Analysis und der Geometrie. Sie erweisen sich als elegantes Mittel zum Lösen von Gleichungen in der Mathematik, aber auch zum Mathematisieren von Problemen aus Physik und Technik. Als Vektoren in der Ebene wie als Drehstreckung dienen sie ebenso der Veranschaulichung geometrischer Objekte.
Diese Buch führt anschaulich in die Arithmetik komplexer Zahlen ein und behandelt umfassend ihre Rolle sowohl beim Lösen von Gleichungen wie auch in der Geometrie der Ebene. Dabei werden ebenfalls Bezüge zur historischen Entwicklung zentraler mathematischer Resultate thematisiert. Übungsaufgaben mit Lösungen zu den einzelnen Kapiteln sowie ein Anhang zum Rechnen mit komplexen Zahlen und konformen Abbildungen in MAPLE komplettieren das Buch.
Diese dritte Auflage wurde um Abschnitte zur nichteuklidischen Geometrie und einer Vorstellung des Programms Cinderella zur Analyse und Visualisierung geometrischer Konstruktionen erweitert. Weiterhin sind in der neuen Auflage zahlreiche Farbabbildungen enthalten.

Inhalt:
Komplexe Zahlen und ihre geometrische Darstellung
Primzahlen im Komplexen
Lösungen algebraischer Gleichungen
Fundamentalsatz der Algebra
Riemannsche Kugel
Komplexe Funktionen
Gebrochen lineare Funktionen
Die Jukowski-Funktion und die Funktion w = z^2
Nichteuklidische Geometrie
Komplexe Zahlen und dynamische Geometrie
Komplexe Zahlen und Konforme Abbildungen mit MAPLE


About the Author:

Joachim Engel, Andreas Fest, Pädagogische Hochschule Ludwigsburg.


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Product Details
  • ISBN-13: 9783110406863
  • Publisher: De Gruyter
  • Publisher Imprint: de Gruyter
  • Height: 244 mm
  • No of Pages: 225
  • Series Title: de Gruyter Studium
  • Weight: 417 gr
  • ISBN-10: 3110406861
  • Publisher Date: 21 Mar 2016
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 170 mm


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