Advertisement

Implicit function theorems and differentiable maps

  • M. H. Protter
  • C. B. MorreyJr.
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Suppose we are given a relation in ℝ2 of the form
$$F\left( {x,{\rm{ }}y} \right){\rm{ }} = {\rm{ }}0$$
(14.1)
Then to each value of x there may correspond one or more values of y which satisfy (14.1)—or there may be no values of y which do so. If I = {x: x 0 — h < x < x 0 + h} is an interval such that for each xI there is exactly one value of y satisfying (14.1), then we say that F(x, y) = 0 defines y as a function of x implicitly on I. Denoting this function by f, we have F[x, f(x)] = 0 for x on I.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • M. H. Protter
    • 1
  • C. B. MorreyJr.
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations