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Mappings and Vector Fields

  • George聽P贸lya
  • Gabor聽Szeg枚
Part of the Springer Study Edition book series (SSE)

Abstract

If we associate each point z of some domain 饾攪 of the z-plane with a certain complex value w according to a given law then w is called a function of z. Two geometrical interpretations of the functional relation are particularly useful. One uses one plane, the other two planes. The value w belonging to the point z (or, if more expedient, \(\bar w\) ) can be thought of as a vector acting on the point z ; in this way a vector field is defined in the domain 饾攪. In the other interpretation, the value w associated with the point z in the z-plane is conceived as a point in another complex plane (w-plane). In this way the domain 饾攪 is mapped onto a certain point set of the w-plane.

Keywords

Vector Field聽Unit Disk聽Level Line聽Stream Line聽Positive Real Axis聽
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

漏聽Springer-Verlag Berlin Heidelberg聽1972

Authors and Affiliations

  • George聽P贸lya
    • 1
  • Gabor聽Szeg枚
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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