The Fundamental Theorem of Gradients | Multivariable Calculus

[@FoolishChemist]

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[@harrys2331]

I love Calculus III so much.

[@johnstuder847]

Another great video - you have a gift for making murky topics so clear. Thank you!

[@friedrichfreigeist3292]

I mean there is nothing wrong with your video, but as a physicist I shiver at the way you write things 😆Great Video!

[@anneallison6402]

What do you mean?

[@EjayB]

Perfect video, and fantastic explanation

[@erenerdem4657]

We love you as math community, keep good work up!

[@danilosiervi]

please continue doing these videos. they help a lot

[@overanalyzed5258]

I really wish the rest of this playkist was out my midterm is on Wednesday and this is so much more helpful AND ENTERTAINING than the explanations I've seen so far. SO MANY PEOPLE MAKE MATH BORING, you do not, thank you

[@johnstuder847]

FYI - this video is not currently part of your math playlist?

[@timbuktu8886]

Dayum bro, thank you! Excellent presentation, I finally start to understand! Please keep the videos coming!

[@overanalyzed5258]

This is extremely good

[@stachuuu2955]

Are you reading my mind? I was just looking for a video like this!

[@eight549]

just a minor nit pick at 8:00, the projection is divided by the norm squared. *b* dot *a* over norm *a* is only the component of *b* in *a* 's direction. In other words, how much the unit vector in *a* direction is scaled. Hence, the extra division by norm of *a*

[@user-mf7li2eb1o]

Thank you very much for this video❤

[@orngng]

For the proof at the end once you expand the dot product you can use chain rule for partial derivatives properties to get a single derivative Then use fundamental theorem of calculus to get the right hand side of the original theorem (For my workings I used r'(t) = (dx/dt, dy/dt, dz/dt))

[@kateseo8917]

Thank you

[@RodneyYe]

Can you please make a video explanation of surface integrals? ⊙∀⊙ Your math is really great! Also exterior derivatives, gradients, curl and divergence, I really like you, wish you good luck

[@FoolishChemist]

Coming up soon 🫡

[@ivaniliev929]

What tablet are you using?

[@FoolishChemist]

An iPad!

[@edbush1415]

Isn't dr/ds the unit tangent vector, whilst dr/dt the actual tangent vector ?

[@therealone2418]

SHIT , GOD DAMN EFFICIENT

[@ranalush]

so im not the only one writing like this

[@user-mf7li2eb1o]

11:46 WHAT ARE YOU DOING??? THIS IS ILLEGAL

[@VXNCT_Official]

bruh it's just the chain rule

[@user-mf7li2eb1o]

Please make another example. It seems everyone is using a circle…