Homotopy Type Theory directional derivative > history (Rev #2, changes)

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Definition

Given a calculus field? FF of scalars scalars, and let a type of indices I V I V , one be could define aFF-calculus vector space? VF I V \coloneqq F^I , with and canonical let function e f:IVF e:I f:V \hookrightarrow \to V F . Let be af:VFf:V \to F be a directionally differentiable function valued in scalars, scalars. and Given given a vectorw:Vw:V, the directional derivative w\Del_{w} is pointwise defined as

w(f)(v)lim (x,y)(x,x)f(v+xw)f(v+yw)xy\Del_{w}(f)(v) \coloneqq \lim_{(x, y) \to (x, x)} \frac{f(v + x w) - f(v + y w)}{x - y}

See also

Revision on April 16, 2022 at 17:36:45 by Anonymous?. See the history of this page for a list of all contributions to it.