Angewandte Mathematik, Modellbildung und Informatik
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Angewandte Mathematik, Modellbildung und Informatik: Eine Einführung für Lehramtsstudenten, Lehrer und Schüler. Mit Java-Übungen im Internet von Thorsten Grahs

Angewandte Mathematik, Modellbildung und Informatik: Eine Einführung für Lehramtsstudenten, Lehrer und Schüler. Mit Java-Übungen im Internet von Thorsten Grahs


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About the Book

Es macht wenig Sinn, gerade wenn man an die Schulen denkt, Numerische Mathematik als Selbstzweck zu prasentieren. Wo ist der Sinn von Interpolation, Approximation und der Losung linearer Systeme, wenn man nicht weiss, in welch vielfaltigen Problemen diese Techniken anwendbar sind? Bei der Suche nach Anwendungen stosst man auf die Modellierung technischer, biologischer und okonomischer Fragen. Des Weiteren muss das Modell in irgendeiner Form auf einem Rechner abgebildet werden, wozu man einige Kenntnisse aus der Informatik benotigt.

Table of Contents:
1 Modellbildung oder: Wie hätte Leonardo modelliert?.- 1.1 Das konzeptionelle Modell.- 1.2 Das mathematische Modell.- 1.3 Das numerische Modell.- 1.4 Ein Beispiel.- 1.5 Der Modellierungszyklus.- 2 Wie schnell wächst der Fußpilz?.- 2.1 Ein einfaches Modell.- 2.2 Ein realistischeres Modell.- 2.3 Weitere diskrete Modelle.- 3 Wie wirtschaftlich ist mein Betrieb?.- 3.1 Modellierung der Geschäftsdaten.- 3.2 Exkurs: Interpolation mit Polynomen.- 3.3 Exkurs: Nullstellensuche.- 4 Wie sendet Asterix Geheimbotschaften an Teefax?.- 4.1 Ein Verschlüsselungsmodell.- 4.2 Bemerkungen.- 5 Was haben Tomographie und Wasserleitungen gemeinsam?.- 5.1 Computertomographie.- 5.2 Ein Rohrleitungsnetz.- 5.3 Der Gaußsche Algorithmus.- 5.4 Zurück zur Modellierung.- 5.5 Iterative Methoden.- 6 Wie fließt der Straßenverkehr?.- 6.1 Eine Frage der Betrachtung.- 6.2 Das Geschwindigkeitsfeld.- 6.3 Geschwindigkeit, Verkehrsfluss und Verkehrsdichte.- 6.4 Partielle Differenzialgleichungen.- 7 Dem Zufall keine Chance?.- 7.1Zur Berechnung von Fläche und Volumen.- 7.2 Die Mathematik des Zufalls.- 7.3 Numerische Berechnung von Wahrscheinlichkeiten.- 7.4 Mehrdimensionaler Zufall.- 7.5 Wie werde ich zufällig?.- 7.6 Fortpflanzung und Genetik.- 8 Wie fängt der Hai die Beute?.- 8.1 Das Lotka-Volterra-Modell.- 8.2 Eine qualitative Analysis.- 8.3 Numerische Modellierung.- 8.4 Ein diskretes Räuber-Beute-Modell.- 8.5 Mahnende Worte.- Literatur.

About the Author :
Prof. Dr. Thomas Sonar ist Professor für Technomathematik am Institut für Analysis der TU Braunschweig.


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Product Details
  • ISBN-13: 9783528031794
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 190 mm
  • No of Pages: 237
  • Sub Title: Eine Einführung für Lehramtsstudenten, Lehrer und Schüler. Mit Java-Übungen im Internet von Thorsten Grahs
  • ISBN-10: 3528031794
  • Publisher Date: 27 Sep 2001
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 125 mm


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Angewandte Mathematik, Modellbildung und Informatik: Eine Einführung für Lehramtsstudenten, Lehrer und Schüler. Mit Java-Übungen im Internet von Thorsten Grahs
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Angewandte Mathematik, Modellbildung und Informatik: Eine Einführung für Lehramtsstudenten, Lehrer und Schüler. Mit Java-Übungen im Internet von Thorsten Grahs
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