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Functions of Several Variables and Their Derivatives

  • Richard Courant
  • Fritz John
Chapter
  • 3.4k Downloads
Part of the Classics in Mathematics book series (CLASSICS)

Abstract

The concepts of limit, continuity, derivative, and integral, as developed in Volume I, are also basic in two or more independent variables. However, in higher dimensions many new phenomena, which have no counterpart at all in the theory of functions of a single variable, must be dealt with. As a rule, a theorem that can be proved for functions of two variables may be extended easily to functions of more than two variables without any essential change in the proof. In what follows, therefore, we often confine ourselves to functions of two variables, where relations are much more easily visualized geometrically, and discuss functions of three or more variables only when some additional insight is gained thereby; this also permits simpler geometrical interpretations of our results.

Keywords

Partial Derivative Boundary Point Tangent Plane Chain Rule Homogeneous Function 
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

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Richard Courant
    • 1
  • Fritz John
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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