Math 2.0

Functional analysis Infinite-dimensional calculus, measures and holomorphy Concept

Fréchet derivative

Builds on Total derivative

Summary

The Fréchet derivative of a map ff between normed vector spaces at a point xx is a bounded linear map. It best approximates f(x+h)−f(x)f(x + h) - f(x) for small hh. It extends the derivative of one-variable calculus to maps between normed spaces, which can have infinite dimension. For maps between Euclidean spaces it is the total derivative.

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  1. Euclidean space object
  2. Total derivative concept
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24 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative, lead section
About this page
Tag06EH97V2A7
URIm2://06EH97V2A7
Aliasesfrechet-derivative, strong-derivative
Kindconcept
WritingW1 stated
MSC46G05
UsesTotal derivative
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