2d curl intuition
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it when asking for an intuitive, visual interpretation of curl after a broken link in an accepted answer.
Recommended by 1 people across 1 different months, 2016 to 2024.
What it is
A short Khan Academy video, narrated by Grant Sanderson, that builds intuition for the curl of a 2D vector field by relating the field to the rotation of a fluid. It is the first in a Khan Academy sequence on curl in multivariable calculus.
What people said
Recommends AXO · 2019-09 · Mathematics Stack Exchange · on “Could you a give a intutive interpretation of curl?”
The link in the accepted answer is broken so here are some videos that I found: Divergence and curl: The language of Maxwell's equations, fluid flow, and more [LINK] (by 3Blue1Brown [LINK] ) A few more videos on Khan Academy > Math > Multivariable calculus > Derivatives of multivariable functions > Curl [LINK] including: 2d curl intuition [this video] 2d curl formula [LINK] 2d curl example [LINK] 2d curl nuance [LINK] Describing rotation in 3d with a vector [LINK] 3d curl intuition, part 1 [LINK] 3d curl intuition, part 2 [LINK] 3d curl formula, part 1 [LINK] 3d curl formula, part 2 [LINK] 3d curl computation example [LINK]
Cites Conor Cosnett · 2016-07 · Mathematics Stack Exchange · on “Can anyone tell me the formula for this vector field?”
3Blue1Brown's video on curl [this video] [LINK] $$V=\bigg[ \begin{array}{ccc} P\left(x,y\right) \\ Q\left(x,y\right) \end{array} \bigg] $$ $P$ gives you the x component at all points in space. $Q$ gives you the y component at any point in space. What is the explicit formula for the above vector field? vortexes at $(6,0)$, $(-6,0)$, $(0,6)$, $(0,-6)$ and a source and a sink at the origin. symmetrical Hints, links welcome
Cites pkskyStacked · 2024-01 · Mathematics Stack Exchange · on “Test for rotational component in arbitrary matrix”
I am studying differential forms and I am trying to characterize exterior derivatives. This journey keeps taking me back to linear algebra and my most recent insight has been the Singular Value Decomposition [LINK] where any rectangular matrix can be decomposed into two rotational matrices and a diagonal matrix. There is an excellent YouTube video that illustrates this by Visual Kernel. [LINK] The whole video series that precedes the SVD video also characterizes some important fundamental types of matrices, orthogonal, diagonal and symmetric. These are easy to identify. But I suspect that it might be possible to identify an arbitrary matrix as having some rotational component without decompo