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Home > Science, Technology & Agriculture > Technology: general issues > Engineering: general > Höhere Analysis mit DERIVE: Mit zahlreichen Abbildungen, Beispielen und übungsaufgaben sowie Mustersitzungen mit DERIVE
Höhere Analysis mit DERIVE: Mit zahlreichen Abbildungen, Beispielen und übungsaufgaben sowie Mustersitzungen mit DERIVE

Höhere Analysis mit DERIVE: Mit zahlreichen Abbildungen, Beispielen und übungsaufgaben sowie Mustersitzungen mit DERIVE


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About the Book

Dieses Buch stellt die Fortsetzung des Bandes "Mathematik mit DERIVE" dar, das der Autor zusammen mit Adi-Ben Israel und R. P. Gilbert geschrieben hat. Die ausgewahlten Themen umfassen den Stoff, den jeder Mathematik- und Ingenieurstudent aus der mehrdimensionalen Analysis kennen sollte. Dabei unterstutzen ihn einerseits viele Ubungsaufgaben, andererseits Mustersitzungen mit dem Computeralgebra-System DERIVE, damit der Blick auf die mathematischen Inhalte nicht durch (zu-)viel Rechnerei verstellt wird.

Table of Contents:
1 Metrische Räume und Stetigkeit.- 1.1 Konvergenz in metrischen Räumen.- 1.2 Topologie metrischer Räume.- 1.3 Stetige Funktionen zwischen metrischen Räumen.- 1.4 Stetigkeit von Vektorfunktionen mehrerer Variablen.- 2 Mehrdimensionale Differentiation.- 2.1 Partielle Differenzierbarkeit.- 2.2 Differenzierbarkeit mehrdimensionaler Punktionen.- 2.3 Taylorsche Formel.- 2.4 Lokale Extrema.- 3 Implizite Funktionen und Iteration.- 3.1 Implizite Punktionen zweier Variablen.- 3.2 Iteration in metrischen Räumen.- 3.3 Implizite Punktionen mehrerer Variablen.- 4 Gewöhnliche Differentialgleichungen.- 4.1 Explizite Differentialgleichungen erster Ordnung.- 4.2 Elementare Lösungstechniken.- 4.3 Differentialgleichungen höherer Ordnung.- 5 Kurven im $$ {\mathbb{R}^n} $$.- 5.1 Parameterdarstellungen von Kurven.- 5.2 Kurven und Tangenten.- 5.3 Rektifizierbarkeit und Kurvenlänge.- 5.4 Funktionen mit beschränkter Variation.- 5.5 Riemann-Stieltjes-Integrale.- 5.6 Kurvenintegrale.- 6 Mehrdimensionale Integration.- 6.1 Integration über Quader.- 6.2 Iterierte Integrale und der Satz von Fubini.- 6.3 Integration über Jordan-meßbare Mengen.- 6.4 Der Transformationssatz.- 7 Integralsätze.- 7.1 Der zweidimensionale Integralsatz von Gauß.- 7.2 Dreidimensionale Flächen.- 7.3 Der dreidimensionale Integralsatz von Gauß.- 7.4 Der Satz von Stokes.- Literatur.- Symbolverzeichnis.- Derive Stichwortverzeichnis.- Stichwortverzeichnis.

About the Author :
Dr. habil. Wolfram Koepf forscht im Bereich der Computeralgebra am Konrad-Zuse-Zentrum für Informationstechnik, Berlin. Er ist Mitautor des Buches "Mathematik mit DERIVE" (Vieweg 1993).


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Product Details
  • ISBN-13: 9783528065942
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 229 mm
  • No of Pages: 206
  • Sub Title: Mit zahlreichen Abbildungen, Beispielen und übungsaufgaben sowie Mustersitzungen mit DERIVE
  • ISBN-10: 352806594X
  • Publisher Date: 01 Jan 1994
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 162 mm


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Höhere Analysis mit DERIVE: Mit zahlreichen Abbildungen, Beispielen und übungsaufgaben sowie Mustersitzungen mit DERIVE
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