IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4613-8958-3_5.html
   My bibliography  Save this book chapter

Relations Between Surface and Volume Integrals

In: Introduction to Calculus and Analysis

Author

Listed:
  • Richard Courant

    (New York University, Courant Institute of Mathematical Sciences)

  • Fritz John

    (New York University, Courant Institute of Mathematical Sciences)

Abstract

The multiple integrals discussed in the previous chapter are not the only possible extension of the concept of integral to more than one independent variable. Other generalizations arise from the fact that regions of several dimensions may contain manifolds of fewer dimensions and that we can consider integrals over such manifolds. Thus, for two independent variables, we considered not only the integrals over two-dimensional regions but also integrals along curves, which are one-dimensional manifolds. With three independent variables, besides integrals over three-dimensional regions and integrals along curves, we encounter integrals over curved surfaces. In the present chapter we shall introduce surface integrals and discuss the mutual relations between integrals over manifolds of varying dimensions1.

Suggested Citation

  • Richard Courant & Fritz John, 1989. "Relations Between Surface and Volume Integrals," Springer Books, in: Introduction to Calculus and Analysis, chapter 0, pages 543-653, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8958-3_5
    DOI: 10.1007/978-1-4613-8958-3_5
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-1-4613-8958-3_5. 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.