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The Derivative

  • Vilmos Komornik
Chapter
  • 2.2k Downloads
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

The classical definition (see Fig. 4.1)
$$\displaystyle{ f'(a):=\lim _{x\rightarrow a}\frac{f(x) - f(a)} {x - a} }$$
of the derivative remains meaningful for vector-valued functions \(f: \mathbb{R}\hookrightarrow Y\). For functions \(f: X\hookrightarrow \mathbb{R}\) of vector variables, however, the fraction is undefined if \(\mathop{\mathrm{dim}}\nolimits X > 1\). But there exist two equivalent definitions that may be adapted to these cases.

Keywords

Orthonormal Basis Column Vector Normed Space Differentiable Function Geometric Meaning 
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.

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Vilmos Komornik
    • 1
  1. 1.Department of MathematicsUniversity of StrasbourgStrasbourgFrance

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