Taylor Theorems and Applications

  • Rodney Coleman
Part of the Universitext book series (UTX)


In elementary calculus we learn certain polynomial approximations of a real-valued function in the neighbourhood of a point. These depend on the degree of differentiability of the function and, given certain conditions, it is possible to bound or estimate the error. The aim of this chapter is to generalize these approximations to mappings between normed vector spaces. In the case where the function concerned is a real-valued function defined on an open subset of \({\mathbb{R}}^{n}\), we obtain a polynomial approximation, with the polynomial being in several variables.


  1. 6.
    Cartan, H.: Differential Calculus. Kershaw Pub. Co., London (1983)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Rodney Coleman
    • 1
  1. 1.Laboratoire Jean KuntzmannGrenobleFrance

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