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Developments and Applications of the Differential Calculus

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

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.

Suggested Citation

  • Richard Courant & Fritz John, 1989. "Developments and Applications of the Differential Calculus," Springer Books, in: Introduction to Calculus and Analysis, chapter 0, pages 218-366, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8958-3_3
    DOI: 10.1007/978-1-4613-8958-3_3
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