Einführungskurs Höhere Mathematik
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Einführungskurs Höhere Mathematik: Folgen, Reihen, Grenzwerte(uni-script)

Einführungskurs Höhere Mathematik: Folgen, Reihen, Grenzwerte(uni-script)


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About the Book

Dieser vierte Band geht naher auf ausgewahlte Themen ein. Uber den Reihen- und den Grenzwertbegriff sowie uber den in den fruheren Banden dargelegten Funktions- und Ableitungsbegriff wird die Taylorreihe erklart. Auch das Integral von Taylorreihen wird behandelt. Ein zweites Themengebiet ist die Wahrscheinlichkeitsrechnung. Neben einer Einfuhrung werden verschiedene Wahrscheinlichkeitsverteilungen behandelt. Wie in allen Banden wird das Gelernte durch ausgewahlte Ubungsaufgaben vertieft. Der Band kann Studierenden angeboten werden, sobald die Grundlagen der Differential- und Integralrechnung behandelt worden sind. Er baut auf dem ersten und zweiten Band des Einfuhrungskurses auf.

Table of Contents:
1 Reihen.- 1.1 Folgen.- 1.2 Reihen.- 1.3 Test für alternierende Reihen.- 1.4 Der Integraltest.- 1.5 Der Vergleichstest und der Quotiententest.- 1.6 Absolute Konvergenz.- 1.7 Das Rechnen mit Potenzreihen.- 1.8 Zusammenfassung.- Testaufgaben zu Kapitel 1.- Übungen zu Kapitel 1.- 2 Taylorsche Reihe und der Zuwachs einer Funktion.- 2.1 Höhere Ableitungen und der Zuwachs einer Funktion.- 2.2 Taylorsche Reihe.- 2.3 Die Differentialgleichung der harmonischen Bewegung.- 2.4 Der Fehler bei der Abschätzung eines bestimmten Integrals.- 2.5 Der binomische Lehrsatz für beliebige Exponenten.- 2.6 Taylorsche Reihen für f (x; y).- 2.7 Zusammenfassung.- Testaufgaben zu Kapitel 2.- Übungen zu Kapitel 2.- 3 Das Moment einer Funktion.- 3.1 Arbeit.- 3.2 Die Kraft auf einen Damm.- 3.3 Das Moment einer Funktion.- 3.4 Zusammenfassung.- Testaufgaben zu Kapitel 3.- Übungen zu Kapitel 3.- 4 Mathematische Modelle.- 4.1 Grundbegriffe der Wahrscheinlichkeitsrechnung.- 4.2 Wahrscheinlichkeitsverteilungen.- 4.3 Die Exponentialverteilung (Poissonverteilung) des zufälligen Verkehrs.- 4.4 Zusammenfassung.- Testaufgaben zu Kapitel 4.- Andere Modelle.- Übungen zu Kapitel 4.- 5 Das Vertauschen von Grenzwerten.- 5.1 Die Gleichheit von fxy und fyx.- 5.2 Die Ableitung von $$\int\limits_a^b {f\left( {x;y} \right)dx} $$ nach y.- 5.3 Differentiation und Integration von Potenzreihen.- 5.4 Das Vertauschen von Grenzwerten.- 5.5 Zusammenfassung.- Lösungen ausgewählter, ungeradzahliger Übungen und Testaufgaben.- 1 Reihen.- 2 Taylorsche Reihe und der Zuwachs einer Funktion.- 3 Das Moment einer Funktion.- 4 Mathematische Modelle.- 5 Zusammenfassung.- Sachwortverzeichnis.

About the Author :
Prof. Dr. Sherman K. Stein lehrt an der University of California. Über die Bearbeiter: Prof. Dr. Angelika Erhardt-Ferron und Prof. Dr. Hildebrand Walter lehren an der Fachhochschule Offenburg und haben als Bearbeiter diesen Kurs zusammengestellt.


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Product Details
  • ISBN-13: 9783528074265
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 244 mm
  • No of Pages: 94
  • Returnable: N
  • Sub Title: Folgen, Reihen, Grenzwerte
  • ISBN-10: 3528074264
  • Publisher Date: 28 Aug 1997
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Series Title: uni-script
  • Width: 170 mm


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Einführungskurs Höhere Mathematik: Folgen, Reihen, Grenzwerte(uni-script)
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