Vector Calculus - Gradient, Divergence and Curl Explained

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Introduction to vector calculus! A look at the gradient, divergence and curl. An important part of university physics and mathematics.
Important Note: The gradient operator can only act on a scalar field.
Vector animation credit: Falstad, check it out:

Chapters:
00:00 Intro
01:42 Scalar Product
06:00 Vector Product
08:56 The gradient
14:00 Divergence
17:32 The Curl
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Complete, Concise & as simple as possible.
great material right here.

zaynbashtash
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In divergence, is multiplication of a derivative operator and a function, which in this case a component of a vector field, equal to derivative of that function or it's just by definition ?

tenburger