Elementare Analysis by Andreas Ba1/4chter - Bookswagon
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Elementare Analysis

Elementare Analysis

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About the Book

1 Einleitung.- 1.1Was ist "Elementare Analysis'?.- 1.2 Wie ist dieses Buch aufgebaut?.- 1.3 Was ist bei der Lektüre dieses Buchs zu beachten?.- 2 Funktionale Zusammenhänge und Funktionen.- 2.1 Funktionale Zusammenhänge.- 2.2 Funktionen.- 2.3 Grundvorstellungen und Darstellungen von Funktionen.- 2.4 Elementare Funktionstypen und ihre Charakteristika.- 2.5 Exkurs: Funktionen und Kurven.- 3 Ein anschaulicher Zugang zu Differenzial-und Integralrechnung.- 3.1 Ableiten: Änderungsraten als fundamentale Idee.- 3.2 Integrieren: Rekonstruktion als fundamentale Idee.- 3.3 Anschaulicher Zusammenhang von "Ableiten' und "Integrieren'.- 3.4 Grenzender Anschauung.- 4 Mathematische Grundlagen der Analysis.- 4.1 Die vollständige Zahlengerade: reelle Zahlen.- 4.2 Folgen und ihre Grenzwerte.- 4.3 Grenzwerte von Funktionen und Stetigkeit.- 5 Grenzwerte von Differenzenquotienten: die Ableitung.- 5.1 Die Ableitung an einer Stelle und die Ableitungsfunktion.- 5.2 Berechnung von Ableitungen und Ableitungsregeln.- 6 Grenzwerte von Riemann'schen Summen: das Integral.- 6.1 Anschaulicher Standpunkt aus Kapitel 3.- 6.2 Das bestimmte Integral und Integralfunktionen.- 6.3 Erste Berechnungen von ("einfachen') Integralen.- 7 Zusammenhang von Differenzial-und Integralrechnung.- 7.1 Stammfunktionen und Richtungsfelder.- 7.2 Der Hauptsatz der Differenzial-und Integralrechnung.- 7.3 Integrieren bedeutet auch Mitteln.- 7.4 Von Ableitungsregeln zu Integrationsregeln.- 8 Anwendungen in Theorie und Praxis.- 8.1Funktionenuntersuchen.- 8.2Das Wechselspiel von Theorie und Anwendungen.- Literaturverzeichnis.- Index
About the Author:

Andreas Büchter, Dipl.-Math., arbeitet als Referent im Ministerium für Schule und Weiterbildung des Landes Nordrhein-Westfalen.

Prof. Dr. Hans-Wolfgang Henn lehrt und forscht am Institut für Entwicklung und Erforschung des Mathematikunterrichts der Technischen Universität Dortmund.

Beide Autoren sind in der Lehrerfortbildung aktiv, haben zahlreiche elementarmathematische und mathematikdidaktische Publikationen veröffentlicht und Lernmaterialien für den Mathematikunterricht der Sekundarstufen entwickelt.


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Product Details
  • ISBN-13: 9783827420916
  • Publisher: Spektrum Akademischer Verlag
  • Binding: Paperback
  • Height: 231 mm
  • No of Pages: 352
  • Series Title: Mathematik Primar- Und Sekundarstufe
  • Sub Title: Von Der Anschauung Zur Theorie
  • Width: 150 mm
  • ISBN-10: 3827420911
  • Publisher Date: 05 Mar 2010
  • Edition: 1
  • Language: German
  • Returnable: N
  • Spine Width: 18 mm
  • Weight: 544 gr


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