IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-658-00285-5_2.html
   My bibliography  Save this book chapter

Analysis

In: Springer-Handbuch der Mathematik I

Author

Listed:
  • Eberhard Zeidler

    (Max-Planck-Institut für Mathematik, Naturwissenschaften)

Abstract

Zusammenfassung Data aequatione quotcunque fluentes quantitae involvente fluxiones invernire et vice versa. (Newton in einem Brief an Leibniz im Jahre 1676) Im Mittelpunkt der Analysis steht die Untersuchung von Grenzwerten. Viele wichtige mathematische und physikalische Begriffe lassen sich durch Grenzwerte definieren, z. B. Geschwindigkeit, Beschleunigung, Arbeit, Energie, Leistung, Wirkung, Volumen und Oberfläche eines Körpers, Länge und Krümmung einer Kurve, Krümmung einer Fläche usw. Das Herzstück der Analysis stellt die von Newton (1643–1727) und Leibniz (1646–1716) unabhängig voneinander geschaffene Differential- und Integralrechnung dar. Bis auf wenige Ausnahmen waren der antiken Mathematik der Begriff des Grenzwerts fremd. Heute stellt die Analysis eine wichtige Grundlage der mathematischen Beschreibung der Naturwissenschaften2 dar (vgl. Abb. 1.1). Ihre volle Kraft entfaltet jedoch die Analysis erst im Zusammenwirken mit anderen mathematischen Disziplinen, wie zum Beispiel Algebra, Zahlentheorie, Geometrie, Stochastik und Numerik.

Suggested Citation

  • Eberhard Zeidler, 2013. "Analysis," Springer Books, in: Eberhard Zeidler (ed.), Springer-Handbuch der Mathematik I, edition 127, chapter 1, pages 215-620, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-00285-5_2
    DOI: 10.1007/978-3-658-00285-5_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-658-00285-5_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.