Calculus 3 Lecture 15.2: How to Find Divergence and Curl of Vector Fields

Calculus 3 Lecture 15.2: How to Find Divergence and Curl of Vector Fields: An explanation of what Divergence and Curl mean and how to find them for Vector Fields.

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[patrickwagner]

This video is 7 years old but still is a better lecture than my current professor could teach me. Thank you professor Leonard

[tauceti]

Divergence & The different cases: (0:00 - 8:50)
Divergence - A measurement of how much *fluid/flow enters* the neighborhood around "P" compared to how much leaves.
> If more *fluid/flow enters* the neighborhood than *leaves it*, then Divergence will be (-) at "P". Think of this as *fluid/flow Gathering* at the point.
> If the *same* amount of *fluid/flow enters* as *leaves*, then Divergence will be "0" at "P"", *in-compressible*
> If more *fluid leaves* than *enters* then divergence will be + at "P". Think of *fluid leaving* the point called Divergent.
How to Find it (9:00 + )
HAHAHA note Del dot F =/= DelF why? (12:30) Gradiant works with one function, its a vector operator. It tells you what to do. (Defn review to 14:30, Important) 15:07 SCALAR, not Vector because it comes from dot produtct.
***15:43 "Think smaller" A point neighborhood around it. Connected to Topology? Remember put a point draw balls around it.. connected?
0 - In compressible
+ - Divergent

Get your dumbbells out its curl time (16:45)
Curl Measures the tendency of the fluid/flow to rotate within a neighborhood of a point. "How much the paddle spins"

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[Fahimsyd]

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[keldonchase]

28:07 - Example 1
44:06 - Example 2
58:23 - Example 3

[newyorkguy]

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[subhajitchakraborty]

The best interpretation of Divergence and curl I have ever seen . Absolutely brilliant.

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[NaturalManifestation]

It's so nice to see the actual explanation of what this stuff means, in a geometric sense. Thank you.