The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus

[@andrewkoulogeorge2569]

Fantastic video, yet again. The mean on my first midterm at college was a 76 and I got a perfect score because of you!

[@DrTrefor]

That's amazing, congrats!

[@ishaanmanhar7392]

who's here a day before their endsems of Calculus?

[@xentarch]

Lmao called me out

[@amandamoore2868]

I'm here prior to my last midterm of calc III lol so yep, pretty much same

[@mantonrogers1398]

Final in 3 hours

[@hasandogan3510]

Just 20min before

[@AnkitKumar-cr3qs]

Love from India sir

[@continnum_radhe-radhe]

Same 🔥🔥🔥

[@narenmani07]

The real question is...where'd you get that shirt?! (it looks amazing)

[@nuralddd]

This proof is so straightforward. Thank you!

[@Alannnn14]

As a physics student I find it very interesting since I've been wondering about how to "undo" the gradient to find the potential function related to a certain force field , so imagine this might be the answer, isn't it? Sorry for any grammar mistake English is not my first language Btw nice t-shirt.

[@DrTrefor]

Exactly, and indeed we’re going to explore exactly that a bit more in the next video:)

[@muaadakmal511]

Ur class really gives a visual feeling of whats really going on.Superbb.I really love ur classes

[@DrTrefor]

Thank you!

[@Fizikakaalda]

These videos really help me for olymp physics. Thanks.

[@rmbennet]

Damn. you guys are flying. We just finished multiple integration. Starting vector calculus next week.

[@DrTrefor]

haha nice hopefully the whole series will be up in time for you needing it:)

[@hydropage2855]

God I keep coming back to this video. You are fantastic

[@arielfuchs316]

This guy will drag me kicking and screaming to an A in my vector calc class

[@JennieXie-rg2xd]

Love from China sir

[@kandagaddalavenkatakiransu5715]

Love from India , and thanks for saying u used Thomas calculus which is the same used for us in classes I'm from nitw

[@brownruns]

Love your shirt! Do you know where I could buy one?

[@WallaceGromit88]

Where did you get your shirt? It’s pretty cool :P

[@srs.r6354]

Yes....I want one of those...

[@matthewmoser8811]

Dr. Trefor Bazett, thanks. Super clutch

[@user-ye1so7rv8j]

you saved my life

[@juanmanuelmillansanchez8165]

Jajajaja I'll need this for monday, can't thank u enough.

[@satyambhardwaj2289]

it's "haha" for god's sake

[@DrTrefor]

Good luck!

[@tomatrix7525]

@@satyambhardwaj2289 It might be German or Dutch or something like that where ja means yes

[@eszentmiklossy]

Just a thought but adding differential forms as an extension of Stoke's Theorem could really help. It was in my calc 4 course and really helped me solidify the ideas. Thanks for all your help this semester!

[@ES-qe1nh]

!!! he should do this, only thing is that it requires some more rigor than what is assumed in these courses

[@SouravBagchigoogleplus]

Nice T-shirt sir.

[@imaginary8168]

Hi Dr. Trefor Bazett, do you have a link to the book you mentioned? I'm deeply interested in it.

[@bulldawg4498]

Excellent presentation of this topic! You certainly rival Sal Khan ....

[@pratyushraj3916]

Too good😅

[@scrappybuilds]

You're a cool dude, Dr. Bazett

[@DrTrefor]

haha thanks!

[@sirajahmed1705]

Just awsm sir ,, love from India

[@donotbebiased6987]

Nice t shirt

[@ogunsadebenjaminadeiyin2729]

👍

[@MarPabl]

First off nice 👕 it'll be useful to learn some 🆒️🕺🏻💃🏻 moves alongside the corresponding functions beneath 😛 Now regarding the 📽 I 🧡 that you take a theoretical approach with a great presentation & animations to clearly explain the concepts. I would only want to ask you to include just a single & simple ℝ🌎 example to finish understanding the concept. I'll 🗣 you a situation I've faced here. You've got several 📽 where an arc length parameterization in "s" is suggested.... but I'm yet to 👀 how that parametrization is actually done. You even have an example there where you use a function for a ⭕ but that one is parameterized in "t" instead of "s" And for that lack of an example regarding how to actually get the arc length parametrization I find somewhat ℂ to understand how to apply the results you get 😥 Finally... will you cover differential forms which can generalize Green & Stokes theorems 🙏🏻❔

[@DrTrefor]

To get the arclength parameter s(t) this is the integral from a to t of the magnitude of velocity. See the recent vid on curves and parameterizations for more. And yes, stokes is coming soon!

[@MarPabl]

@@DrTrefor yes I 👁️ it, the one you compared driving the 🚗 based on ⏳ or distance... But you didn't calculate any actual parametrization there 😓

[@user-sw4vt3mi9o]

Nice shirt 👕

[@continnum_radhe-radhe]

🔥🔥🔥

[@ileanadominguez6055]

Thank you very much :)

[@ramilawijesuriya7259]

Great !!

[@GoogleUser-ee8ro]

excuse my ignorance, is calculus4 a high school curriculum in US or university level calculus?

[@DrTrefor]

usually its in second year university

[@colbeh]

Nice beard

[@markpadley890]

Another outstanding explanation - you refer to a textbook - could you give me the reference please?

[@physicslover1950]

How to convert vector fields into scalar functions ?

[@DrTrefor]

Coming up in the very next video on Sunday!

[@polarcraftvelocentricbudde4345]

that's a very handy shirt.

[@DrTrefor]

Haha right!?

[@satyambhardwaj2289]

where to buy that t-shirt?

[@DrTrefor]

I can't find he exact one, but I have a link in my description to a similar one

[@jaehaerys9194]

hey, where did scalar field go

[@tarteel_salah9994]

I need that T-shirt

[@a1sharp65]

If a fluid flow field happens (kind of??) due to gravity, how come gravitational fields are conservative but fluid flows are not (from your examples in the previous video) (is this a dumb question?)

[@carultch]

A very interesting question. Conservative only really relates to conservation of energy, when the field specifically is a force field. For fluid flows, the vector isn't force, but rather velocity, so it is completely possible for fluid flows to be non-conservative, or rather rotational, even if the energy source is gravity. One cause of fluid flow fields to become non-conservative, is viscous friction with the boundary, which is an energy sink that sends energy to the thermal domain, so this one way a fluid flow field can become rotational, even if driven by a conservative force. The rotational/irrotational is a much better term pair for describing fluid flow fields, while conservative term is much better for force fields. Pure math uses these terms interchangeably, when the application of the field is not relevant. For force fields to be non-conservative, there has to be an energy source or sink that moves energy out of the domain of the field. Electromagnetism is full of non-conservative fields, because of ways that it can exchange energy back and forth between its two forms. Newtonian gravity is conservative, but relativistic effects can make it non-conservative. Look up gravitomagnetism if you are curious.

[@fadlialim8762]

need your tshirt!

[@SahilKumar-uc8fn]

How can i get these slides?

[@aarohgokhale8832]

5:10 hahaha pun intended?

[@musakarrar9036]

Can you help to solve exercises?

[@sumitkumarsahoo7601]

I don't understand the chain rule part, can we write grad(f)=df/dr where dr is a vector plz clarify

[@richardvalentinonainggolan328]

same here. did you figure it out?

[@sumitkumarsahoo7601]

@@richardvalentinonainggolan328 nope😅