Fundamental Theorem of line integrals

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In this video, I present the fundamental theorem for line integrals, which basically says that if a vector field ha antiderivative, then the line integral is very easy to calculate. This illustrates why conservative vector fields are so important! I also provide a proof of the FTC, which uses... the chen lu!!! Finally, I show why we need the condition P_y = Q_x to check if a vector field is conservative. Enjoy!

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This man's happiness when he does maths just makes me love maths even more

justdusty

So clear! And so short! I never thought that this could be explained so convincing in so little time together with an example.

WerIstWieJesus

Quite possibly the best video I've seen on the topic, thank you!

finnbar

As you say “Thank you for coming”, just want to say “Thank you for teaching”!

miazlorenz

That theorem is very interesting and very useful! Thanks for making this video!

Aviationlover-belugaxl

Dr. Peyam, hope you are doing well! Thank you for all the wonderful content 😊.

lightspd

You should do a video proving the equality of crossed partial derivatives!

TheMauror

at 6:45, dr peyam saying "arrrrgh but this- this is g(y)" is my new favorite thing in the world

bouteilledargile

OMG thank you alot now I understand it!!

aseelal

very good guy, congratulations, your channel is awesome

matheuscolmenero

Important note: this only applies to conservative fields. In non conservative fields the line integral depends on the path.

softwarephil

I have a question, why u didn't after adding at the end in example ignored 2, Does that mean we have to add fx and fy always

irshadsirslectures

Why does Clairaut's theorem (also known as: Swchartz theorem) can be applied when F is conservative?

cafe-tomate

It's dependant of the integration of parametrics functions of blackpenredpen ? If it's the case it's genial ! Thanks.

dgrandlapinblanc

Why when taking a second derivative the order (dxdy <-> dydx) doesn't matter?
They don't teach you that in physics 😿

borg

It was on 420 likes so I didnt want to like but had to give this a like now its 421 😂🤘🤘

jannien

Quixote is a character in a foreign book.

michaelempeigne

im struggling with this stuff
your smile makes me feel bad because i dont get it :(

mathadventuress

Well, i'm sorry dr. Pi but you really had to explain that the first "check" (Schwarz Theorem) is a necessary but not sufficient condition for that to be an exact equation.
"Luckily" enough, that f(x, y) is differentiable and determined for every real x, y :)

Zonnymaka

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