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derivative

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derivative is owned by Robert Milson, Igor Khavkine, Thomas Foregger, Warren Buck, J. Pahikkala, Juan M. Marquez B., bci1, smithpith.

How to Cite This Entry

Robert Milson, Igor Khavkine, Thomas Foregger, Warren Buck, J. Pahikkala, Juan M. Marquez B., bci1, smithpith. "derivative" (version 32). PlanetMath.org. Freely available at http://planetmath.org/Derivative2.html.

Classification

AMS MSC:	26A24 (Real functions :: Functions of one variable :: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems)
	46G05 (Functional analysis :: Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) :: Derivatives)
	26B05 (Real functions :: Functions of several variables :: Continuity and differentiation questions)

Pending Errata and Addenda

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Discussion

Additional Reference by smithpith on 2009-04-25 22:53:30

PlanetMath article: Non-Newtonian calculus.

[ reply | up ]

Derivative as Linear Approximation by joshsamani on 2008-04-13 05:23:40

I understand that the Frechet derivative is a linear approximation in the sense that it is a linear transformation which approximates a function between Banach spaces.

But, I have read in multiple texts that it is the "best" linear approximation. In what sense in the Frechet derivative the "best" linear approximation as opposed to just some linear approximation?

[ reply | up ]

Possible error in formula by dtowell on 2003-12-09 12:13:10

Under Linearity, it seems like there is a typo in the formula, bg(x) becomes bf'(x) which doesn't seem right but its been a long time since I studied this sort of thing so I could be wrong.

Dwayne

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Re: Possible error in formula by Igor Khavkine on 2003-12-09 12:31:19

Norm on L(V,W) by Igor Khavkine on 2002-05-31 17:55:35

I mention in the article above that L(V,W)
can be considered a Banach space itself.

The fact that it is a vector space is trivial.
However, I'm not sure what the canonical norm
for that space is. Perhaps the L^p norm?
What are some other commonly used norms that
turn L(V,W) into a normed space? Do they
generate the same topology as the L^p norm?

[ reply | up ]

Re: Norm on L(V,W) by Igor Khavkine on 2002-06-03 19:42:04

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derivative

How to Cite This Entry

Classification

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Pending Errata and Addenda

Interact

Discussion