curl and divergence (KristaKingMath)

In this video we'll learn how to find the curl and divergence of a vector field using the formulas for curl and divergence.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[michaelngecha]

The math is good and all, but the voice, its heavenly

[princekwakuarhin]

You alongside organic chemistry tutor are the best .God bless you

[dmelnick]

You're the best study partner, by the way.. You got me through Calc 1 and 2, now you're pulling me through calc 3!!! You should be paid LOL!

[TimothyMoananu]

Thank you so much. You have contributed so much with my progress in Engineering Mathematics. I'm very grateful.  

[dae]

Wonderful stuff. As a non physics type I have like many others stared blankly at Maxwell's field equations. Here u not only go through the maths, so elegantly, but u give a clear explanation of what curl and divergence are. many thanks once again.

[billnolastname]

Calc 3 happened many moons ago.  Thanks for the quick, clear refresher.

[jackal]

I try to review complex math once a month to keep myself sharp; you always deliver!

[preventer]

Glad I found this channel. This was a topic I struggled with, but much clearer now. Thanks a million!

[Cikot]

Wow never thought it'd be this easy. thank you! :D

[OverLordOfDardWorld]

Thank you so much for explaining the difference between the formulas!! 8:13

[snowye]

You are a real life saver, our lecture's accent is so bad that none of us understands him

[fabicauseway]

Thank you so much. Your clear and effective voice helped a lot!

[tristan]

This is why I skip math class. Why sit for an hour and not understand when I can watch a 12 min video and be able to do all my homework?

[clementafesi-dei]

straight up, wasnt getting it in class but within 12mins im good

[dmelnick]

Also, if you forget you can think of the operator as a vector, which is the expanded matrix you gave...  ["del" x F = curl F] and ["del" (dot) F = div F] ... they can be thought of as analogous to a dot product and cross product of the operator and F.. This also means div curl = 0 is like a scalar multiple...

[Myrslokstok]

Nice matrix explenation on 11:08!
I will save this link!

[GTMjo]

Something I noticed when you wrote PQR down the left and XYZ across the right: it looks like a Row Reduced Echelon Form (RREF) matrix at 10:29. Does that mean anything? Is it significant in any way or is it just by coincidence ? I would be really amazed if you could apply linear algebra in this part. Makes me wonder if math can be this beautiful or just coincidental.

[EvilCloudStrife]

Thank you so much, you're getting me through college.

[burlapse]

Nice example, glad you posted this during my calc 3 semester! xD

[dingyanhaizi]

very helpful ! btw your handwriting is so good