Fundamental Theorem of line integrals

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!

[@justdusty9697]

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

[@finnbar004]

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

[@drpeyam]

Wow, thanks!

[@WerIstWieJesus]

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

[@miazlorenz8799]

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

[@harryiscool9619]

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

[@faith3174]

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

[@TheMauror22]

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

[@aseelal5338]

OMG thank you alot now I understand it!!

[@lightspd714]

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

[@softwarephil1709]

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

[@matheuscolmenero4493]

very good guy, congratulations, your channel is awesome

[@brandonredenbo6583]

Kyle from Nelk teaches Calc 3

[@borg972]

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

[@LudusYT]

It's something you learn in Calculus 3 (not Physics I believe) called Clairaut's Theorem. In this theorem you can see that those two derivatives are the exact same thing.

[@tomatrix7525]

Experiment with derivatives mixing up the order, you’ll see it does not matter. As to why, well it’s analogious to multiplying. That is, 10.2.5 = 10.5.2 etc

[@dgrandlapinblanc]

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

[@drpeyam]

Those are two slightly different things, unfortunately! Here I show the line integral of a vector field is independent of parametrization. In bprp’s videos he shows a curve is independent of parametrization!

[@dgrandlapinblanc]

@@drpeyam Thank you very much fort your complete answer.

[@TheSouravrocks]

thank you so much!

[@irshadsirslectures4446]

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

[@jannien4129]

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

[@michaelempeigne3519]

Quixote is a character in a foreign book.

[@weinihao3632]

I think he said "quixotic" - which seems to be derived from the character, though :)

[@Zonnymaka]

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 :)

[@mathadventuress]

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

[@drpeyam]

:(

[@drpeyam]

Check out my vector calculus playlist maybe?

[@drpeyam]

And this: sites.uci.edu/ptabrizi/math2ewi20/

[@mathadventuress]

@@drpeyam I'll check it out when I finish this class. My final is Friday yikes.

[@mathadventuress]

@@drpeyam I have a 57% so far lmao I need like a 65% to pass the class with a c