IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-0636-7_13.html
   My bibliography  Save this book chapter

Complex Analysis II: Further Topics

In: Introduction to Mathematical Analysis

Author

Listed:
  • Igor Kriz

    (University of Michigan, Department of Mathematics)

  • Aleš Pultr

    (Charles University, Department of Applied Mathematics (KAM) Faculty of Mathematics and Physics)

Abstract

There are some extremely important concepts in complex analysis which we did not cover in Chapter 10 , and which ultimately lead up to several other areas of mathematics. First of all, quite a bit more can be said about conformal maps. Under very general conditions, one open subset of $$\mathbb{C}$$ can be mapped holomorphically bijectively onto another. We prove one such result, the famous Riemann Mapping Theorem. In many situations, such maps can even be written down explicitly. Those are the Schwartz-Christoffel formulas, which have applications in cartography, as the basic condition on mappings in cartography is to be conformal (since distortion of distances in a topographical map is generally considered more allowable than distortion of angles). Yet, the Schwarz-Christoffel formulas also lead to elliptic integrals, which are “inverse” to elliptic functions (see for example [11]).

Suggested Citation

  • Igor Kriz & Aleš Pultr, 2013. "Complex Analysis II: Further Topics," Springer Books, in: Introduction to Mathematical Analysis, edition 127, chapter 13, pages 311-348, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0636-7_13
    DOI: 10.1007/978-3-0348-0636-7_13
    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:978-3-0348-0636-7_13. 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.