Vector Fields, Divergence, and Curl

We know about vectors, and we know about functions, so we are ready to learn about vector fields. These are like functions that take in coordinates and give back vectors, so there will be a vector associated with every single point in the field. There are two things we must be able to do with vector fields as well, which involve the del operator and either the dot product or the cross product with the vector field. These give us the divergence and the curl of the vector field, respectively. Let's learn all about these operations now.

Script by Howard Whittle

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[shiori]

This 15 minute video was more informative than the 3 hours of lecture videos my school posted for my online class. Thanks for making great content.

[gregkocher]

50 years ago I was wrestling with these functions, especially the visual concepts of divergence and curl. Never once was a concise summary like this was laid out. My career never called upon me to use these but I felt compelled to remaster them in my retirement. And next I will apply them. It's never too late to get the satisfaction of learning.

[saniamuneer]

There is a minor mistake in 9:50 the x^2 is negative otherwise your tutorials are awesome ✨. Thanks for your great effort for making such amazing videos for students like us.

[petercook]

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[Minespidur]

Thanks so much for going into these more advanced topics. Can’t wait for your videos on differential equations

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[janie]

I just found this series and will be using it to help me pass multi variable calculus exam in a few weeks! Thank you

[zakariad]

So clearly explained ! Thank you so much !

[AbdullahBabar-cbtr]

Prof.Dave makes life much easier such great and comprehensive explanation of these concepts.

[truthreveal]

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[buildup]

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[PeteC]

Hey, at 9:40 or so, why did the minuses in the square brackets become pluses when you did the partial differentiation?

[tnpwqiv]

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[uniboy]

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[nameless]

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[katemorris]

You’re a much better teacher than my college professor