Differentiable function of several variables
Summary
A function of several variables is differentiable at a point when, near that point, it is close to a linear function plus a constant. The error is small compared with the distance to the point. The linear function is the total derivative of the function at the point.
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33 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
- 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
- Path independence of line integrals 0BFN21TF5F
- Harmonic function 0DEB0JMN0W
- Laplacian 0E0B6RA8K0
- Closed and exact forms 0F1AVGX26N
- Curl-free field that is not conservative 0GRM3BS0DD
- Divergence theorem on a rectangle in the plane 0GZ3D8F921
- Del operator 0H6DP8CHND
- Scalar potential 0H7C3T1GJY
- Generalised Stokes theorem 0HPHKCGEQ0
- Green's theorem 0HR3N02317
- Vector calculus identities 0JC5X4HWR2
- Saddle point 0JW6MDHAZD
- Divergence theorem 0JX86PSSA9
- Diffeomorphism 0KZZ70ZHXP
- One-form 0MTENFBW3Q
- 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
Sources
- Web https://en.wikipedia.org/wiki/Differentiable_function, Differentiability in higher dimensions
What links here
Definitions
- Differentiable function of several variables 0135XZZQ8M
- Differentiable on an open set 08S7FDRS5Z
Used by
- Tangent plane to a graph 035V802J58
- Gradient 0ABK9V9Y64
- Diffeomorphism 0KZZ70ZHXP
- Partial derivatives do not imply differentiability 0TNZC55X3J