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Developments and Applications of the Differential Calculus

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

Abstract

Frequently in analytical geometry the equation of a curve is given not in the form y = f(x) but in the form F(x, y) = 0. A straight line may be represented in this way by the equation ax + by + c = 0, and an ellipse, by the equation x2/a2 + y2/b2 = 1. To obtain the equation of the curve in the form y = f(x) we must “solve” the equation F(x, y) = 0 for y. In Volume I we considered the special problem of finding the inverse of a function y = f(x), that is, the problem of solving the equation F(x, y) = y—f(x) = 0 for the variable x.

Keywords

Differential Form Tangent Plane Double Point Parametric Representation Differential Calculus 
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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