Vector Calculus #2 | Gradient, divergence, and curl

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What this video covers:

Intro (0:00)

Gradient operator (0:58)

Open sets (2:34)

Example: Computing the gradient (3:19)

Conservative fields (4:45)

Example: Gravitational force (5:04)

Divergence operator (6:20)

Solenoidal fields (8:01)

Fundamental Theorem of Vector Calculus (8:24)

Curl operator (9:06)

Irrotational fields (11:00)

Relationship between conservative and irrotational fields (11:44)

Simply connected sets (13:02)

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What is covered in this series of videos:

Gradient, divergence, and curl operators (video #2 - this video)
Conservative, solenoidal, and irrotational fields (video #2)
Helmholtz’s theorem (Fundamental Theorem of Vector Calculus) (video #2)
Orientability and positive orientation (video #3)
Independence of path (video #6)
Stokes’s Theorem (video #7)

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Prerequisites:

A solid understanding of differential and integral calculus, partial derivatives, and multiple integrals.