Parametrised curve
Summary
A parametrised curve in is a continuous vector-valued function of one real variable, defined on an interval. One can think of the parameter as time and of the curve as the trajectory of a moving point.
What this node needs for W1
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What this needs
To read this node, read these 4 nodes in this order. The foundations come first, and the list ends with this node.
- no evidence level
- Euclidean space object
- Function concept
- Vector-valued function concept
- Parametrised curve concept
What depends on this
32 nodes use this node, directly or through other nodes.
- Exterior derivative 004FRCXH6M
- Line integral of a scalar field 02QJVFCNYD
- Mean value theorem in several variables 03HGK7EW6R
- Closed curve 045YFKRW0P
- 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
- Stokes' theorem 0AKRKVHW94
- Path independence of line integrals 0BFN21TF5F
- Limit along different paths 0BJ6H85DRQ
- Separately continuous but not continuous function 0C0KPAKK9Y
- Work done by a force field 0CDZ684TCD
- Closed and exact forms 0F1AVGX26N
- Curl-free field that is not conservative 0GRM3BS0DD
- Divergence theorem on a rectangle in the plane 0GZ3D8F921
- Line integral of a vector field 0H5MR9B6GT
- Rectifiable curve 0HATW2VWAZ
- Generalised Stokes theorem 0HPHKCGEQ0
- Green's theorem 0HR3N02317
- Divergence theorem 0JX86PSSA9
- One-form 0MTENFBW3Q
- Arc length parametrisation 0Q4CJ5NAT1
- Differential form 0QHTX7WQEY
- Wedge product of forms 0S166D363M
- Gradient theorem 0SD237FEJD
- Partial derivatives do not imply differentiability 0TNZC55X3J
- Regular curve 0V7090SSPC
- Gradient is orthogonal to level sets 0VXYV3NQQ1
- The exterior derivative squares to zero 0X308R2DBE
- Homotopy invariance of line integrals of closed forms 0YVVN6R715
- Tangent vector of a curve 0ZCZK72B45
Sources
- Web https://en.wikipedia.org/wiki/Parametric_equation, lead section
- Web https://en.wikipedia.org/wiki/Differentiable_curve, Definitions
What links here
Used by
- Line integral of a scalar field 02QJVFCNYD
- Closed curve 045YFKRW0P
- Chain rule for a composition with a curve 0A8TJ0VHC7
- Limit along different paths 0BJ6H85DRQ
- Line integral of a vector field 0H5MR9B6GT
- Rectifiable curve 0HATW2VWAZ
- Regular curve 0V7090SSPC
- Tangent vector of a curve 0ZCZK72B45
Definitions
- Parametrised curve 0JF1XXGWB4