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Analysis Mit Dem Computer

Analysis Mit Dem Computer

          
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About the Book

Analysis stellt in der mathematischen Wissenschaft eine 1m 19. Jahrhundert mit großer Strenge entwickelte Theorie dar. Ihre Fundamente ruhen auf dem Grenz- wertbegriff und den axiomatischen Eigenschaften der reellen Zahlen. In der Schule, die sich auf wissenschaftliche Grundbildung beschränken muß, sind m der Analysis explizite Lösungen oft nicht erreichbar, weil hierzu aufwendige Termumformungen oder Abschätzungen nötig sind. Auch erschließt sich auf der Schule nicht die volle Systematik der Satzzusammenhänge und einschlägigen Be- griffe, weil die notwendigen Beweistechniken nicht zur Verfügung stehen. Es wird nicht überraschen, daß der Computer Grenzen dieser Art auch nicht über- winden kann. Allgemeingültige Aussagen auf der Grundmenge der reellen Zahlen kann er grundsätzlich nicht treffen, da ihm nur eine Teilmenge der rationalen Zahlen zur Verfügung steht. Die Feinstruktur einer überall stetigen und nirgendwo differenzierbaren Funktion kann kein Plotter zeichnen und Konvergenz oder Diver- genz einer allgemeinen Folge kann kein Rechenwerk entscheiden. Analysis mit dem Computer gewinnt erst in anderer Sicht ihr Recht. Viele Anwendungsprobleme führen auf empirische Funktionen, welche zu interpolieren, zu approximieren oder auszugleichen sind. Ihre Nullstellen werden ebenso interessieren wie ihre Integrale. Für alle diese Ziele sind seit langem numerische Verfahren bekannt, deren al go- rithmischer und numerischer Aufwand relativ hoch ist. Über das Entlastungsinstru- ment Computer werden diese Verfahren erstmals leicht der Schule zugänglich; zu- gleich gewinnt man damit eine Anwendungsorientierung, welche hoch erwünscht ist, weil sie Mathematik beziehungshaltig macht.


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Product Details
  • ISBN-13: 9783519025283
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Height: 244 mm
  • No of Pages: 241
  • Series Title: Mikrocomputer-Praxis
  • Weight: 394 gr
  • ISBN-10: 3519025280
  • Publisher Date: 01 Feb 1985
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 13 mm
  • Width: 170 mm


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