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Lineare Algebra mit dem Computer: (MikroComputer-Praxis)

Lineare Algebra mit dem Computer: (MikroComputer-Praxis)


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About the Book

Lineare Algebra gehört zu den Grundvorlesungen an Universitäten und Fachhochschulen und ist ein Standardkurs in der gymnasialen Oberstufe. Uber die Kursinhalte herrscht zur Zeit weitgehende Un- zufriedenheit. Diese gründet sich u.a. auf eine zu frühe und oft übertriebene Behandlung von Vektorräumen, sture Rechnerei (etwa bei der Lösung linearer Gleichungssysteme) und fehlenden Reali- tätsbezug. Angesichts dieser Situation wird mit diesem Buch der Versuch gemacht, neue Wege zu gehen: llL Die Lineare Algebra wird konsequent aus problemorientierten, realitätsnahen Ansätzen heraus entwickelt. Durchgehendes Hilfsmittel ist der Matrizenkalkül. ilL Zu zahlreichen Algorithmen werden graphische Darstellungen (Struktogramme) und PASCAL-Programme angegeben, so daß ein geziel- ter Computereinsatz möglich wird. l!L Dabei wird nicht nur gezeigt, wie der Computer als Rechen- hilfsmittel eingesetzt werden kann. Seine Verwendung führt auch zu neuen methodischen Ansätzen und Fragestellungen abseits der bishe- rigen Routineaufgaben, indem z.B. mit unterschiedlichen Datensät- zen experimentiert wird. l2l Die frühzeitige Bereitstellung eines Pakets von Matrizenproze- duren mit Parameterübergaben ermöglicht auch einem im Programmie- ren ungeübten Leser einfache Problemlösungen am Rechner. Wieweit dabei die Prozeduren vom Leser (Schüler im Unterricht) selbst er- arbeitet werden, bleibt ihm selbst überlassen. Sie können ebenso- gut auch als "black-box" benutzt werden. (6) An den nach dem Konzept (1) abgefaßten Lehrgang schließen sich Fallstudien unterschiedlichen Schwierigkeitsgrads an, die an ge- eigneten Stellen des Lehrgangs nach Bedarf eingeschoben werden können. J2l Die Darstellung der Eigenwerttheorie-Grundlagen und der Anwen- dungen von Eigenwerten in den Fallstudien ist so angelegt, daß ei- ne Behandlung auch in der Schule möglich wird.

Table of Contents:
1. Grundlegende Matrizenverknüpfungen.- 2. Matrizeninversion.- 3. Lineare Gleichungssysteme (LGS).- 4. Analytische Geometrie.- 5. Vektorräume.- 6. Matrizenpotenzen.- 7. Grundlagen aus der Eigenwerttheorie.- 8. Populationsdvnamik 1.- 9. Das Stücklistenproblem.- 10. Abrechnungsmatrizen.- 11. Iterative Lösung linearer Gleichungssysteme.- 12. Einige Probleme bei der Lösung linearer Gleichungssysteme mit dem Computer.- 13. Elementare Anwendungen der Eigenwerttheorie.- 13.1 Populationsdynamik 2.- 13.2 Berechnung von Matrizenpotenzen.- 13.3 Ein Problem aus der Abbildungsgeometrie.- 14. Markow-Ketten.- 14.1 Bevölkerungsbewegungen (Grundbegriffe).- 14.2 Warteschlangen (Markow-Ketten mit mehr als 2 Zuständen).- 14.3 Irrfahrten (absorbierende Markow-Ketten).- 14.4 Zusammenfassung, Übungsaufgaben.- Anhang: Grundbegriffe aus der Wahrscheinlichkeitsrechnung.


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Product Details
  • ISBN-13: 9783519025115
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 244 mm
  • No of Pages: 288
  • Returnable: N
  • Width: 170 mm
  • ISBN-10: 3519025116
  • Publisher Date: 01 Mar 1983
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Series Title: MikroComputer-Praxis


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Lineare Algebra mit dem Computer: (MikroComputer-Praxis)
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