Fréchet derivative
Summary
The Fréchet derivative of a map between normed vector spaces at a point is a bounded linear map. It best approximates for small . 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.
What this node needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What depends on this
40 nodes use this node, directly or through other nodes.
- Exterior derivative 004FRCXH6M
- Tangent plane to a graph 035V802J58
- Mean value theorem in several variables 03HGK7EW6R
- Jacobian matrix 047NDTEPCV
- Lagrange multiplier with one constraint 04A2XEX4D4
- Poincaré lemma for one-forms on convex sets 05MC3HND79
- Area of a region as a line integral 09CBQB6V67
- Chain rule for a composition with a curve 0A8TJ0VHC7
- Gradient 0ABK9V9Y64
- Stokes' theorem 0AKRKVHW94
- Strict differentiability 0B6QWX3086
- Path independence of line integrals 0BFN21TF5F
- Harmonic function 0DEB0JMN0W
- Laplacian 0E0B6RA8K0
- Closed and exact forms 0F1AVGX26N
- Iterated derivative 0F32S73FJN
- Total derivative 0FNKFT8H6E
- Curl-free field that is not conservative 0GRM3BS0DD
- Divergence theorem on a rectangle in the plane 0GZ3D8F921
- Del operator 0H6DP8CHND
- Scalar potential 0H7C3T1GJY
- Differentiable function of several variables 0HHHDCXZV4
- Generalised Stokes theorem 0HPHKCGEQ0
- Green's theorem 0HR3N02317
- Vector calculus identities 0JC5X4HWR2
- Saddle point 0JW6MDHAZD
- Divergence theorem 0JX86PSSA9
- Diffeomorphism 0KZZ70ZHXP
- One-form 0MTENFBW3Q
- Derivative of a map into R^n by components 0NS0X75RS1
- Conservative vector field 0PKG97PX9Y
- Differential form 0QHTX7WQEY
- Wedge product of forms 0S166D363M
- Gradient theorem 0SD237FEJD
- Partial derivatives do not imply differentiability 0TNZC55X3J
- Gradient is orthogonal to level sets 0VXYV3NQQ1
- Linear approximation 0W276SSSCG
- The exterior derivative squares to zero 0X308R2DBE
- Homotopy invariance of line integrals of closed forms 0YVVN6R715
- Jacobian determinant 0ZCSMYHTBP
Sources
What links here
Definitions
- Fréchet derivative 08EVNYZF42
Used by
- Strict differentiability 0B6QWX3086
- Iterated derivative 0F32S73FJN
- Total derivative 0FNKFT8H6E