Line Integrals Are Simpler Than You Think

[@77rezaa]

A complicated concept is nicely explained. I loved the domain expansion :)

[@FoolishChemist]

Glad you liked it!

[@DanielTV1213]

@@a.kofficial6140 What a fantastic reference!

[@Deadpoet132]

DOMAIN EXPANSION MULTIVARIABLE 🙏👹

[@FoolishChemist]

🥶🥶🥶

[@AyushKumar-md9ut]

nah, i'd integrate

[@sveps8883]

@@AyushKumar-md9ut wanted ti say that too

[@abdellatifdz8748]

That was sick

[@Wutheheooooo]

​@@AyushKumar-md9ut But would you differentiate? Nah I'd integrate

[@abbasfadhil1715]

Where have u been when i first looked up line integrals this vid made the most sense, u earned a vote (:

[@alsfiend2151]

В спешке проходили криволинейные интегралы в прошлом семестре. Решил глянуть и добить гештальт от вас узнал больше чем на парах. То как вы провоцируете мышление четко обозначая проблему, тем подводя нас к выводу формулы это невероятно!! :)) И не думал, что корни вместо дифференциациалов это эхо теоремы Пифагора

[@literallynull]

Да ничего совковые преподы объяснить не могут. Я от индусов на ютубе больше узнал чем за весь прошлый учебный год. Сейчас ВУЗ в России это просто отсрочка от армии, а не источник знаний.

[@EjayB]

Incredible video man. A million thank yous for going through those parametrisation steps so slowly and clearly!

[@johnstuder847]

Thank you! You have the ability to make math concepts clear. Not sure what it is exactly…the explanation is clear, without too much math lingo. Others explain the material, but for some reason do not ‘connect the dots’ and generalize the concepts. I see this in all of your math videos - not sure if it is deliberate, but I think it really helps when the basic concept is generalized to the more interesting and powerful ‘global’ concept. Examples: in ‘Essence of Multivariable’ you show how many of the vector calculus concepts boil down to just one formula. In the line integral video, you take the concept of parameterization, and generalize it to n dimensions (which I think is novel on KZbin). This is super helpful. I personally really like this approach. But your video titles don’t describe your videos…so those searching for these general descriptions won’t find them. The Essence and Line Integral titles should say something eluding to the generality lurking within, otherwise people think they are just regular videos - which they are not. They are very special and unique, and deserve way more views! I realize you name them this way on purpose - so you don’t scare some viewers off, but maybe create another channel with more general titles which link to the same videos, or maybe use keywords to attract a broader audience? Judging from the comments, many could benefit from your talents, and you deserve more hits! Best of luck to you!

[@FoolishChemist]

Thanks for kind words and the suggestion! I'll try implementing this and see how it improves viewership

[@Phanimations]

With this treasure I summon, divine general Stokes! In all seriousness though, nice vid. Line integrals are weird, and it's hard for some to understand how you transform this formulation into a method suitable for integrating over vector fields.

[@ym-xx6kj]

This video's editing was legendary. Please make more videos I beg you

[@rachelgreene3879]

I was having a hard time visualizing line integrals- But now it makes so much sense! Great video, thanks for uploading!

[@Professional-Hater]

In my first year of ug rn and the gid was soo good that I was able to keep up until the vector valued functions! Great video 👏🏻

[@_C_-l-_-l-]

By far the clearest explanation that I have heard! Nice job!

[@monkeychicken6032]

I've tried multiple videos to introduce me to multi-variable calculus and line integrals and all have failed except for this one, not one single concept not understood. Great video honestly as a student who's still in highschool and addicted to math it's really hard to find good videos about topics this complicated, which I get because less and less people get interested as the topics get harder and harder because of unfamiliarity and the lack of will to learn new concepts. Thanks a lot I hope you can keep making videos like these even though they probably won't do great views wise!

[@willthecat3861]

There;s lots. But a lot are follow the recipe and shake and bake, to get the answer. A cat can do some of that. If you;re just looking for 'how to get the answers' and pass high school math... and that sort of stuff... basically monkeymatics... Khan Academy does a decent job. For a much better presentation...3Blue1Brown, Grant... (former Khan Academy presenter, and the very best part of it) does a better job. But you can spend a lot of time to get to the level of understanding presented there. If you like geometry, and 'visual learning, 3Blue1Brown is the master of it... and one of the first to do it. For a more analytical approach, Dr. Perun is good.

[@matijaderetic3565]

Dr Trefor Bazett made a playlist on vector calculus. I enjoyed watching it.

[@polarjsapkota2484]

This is the best video on line integrals in the Internet right now!

[@swamihuman9395]

- Line integral in vector space of polynomials w/ complex-valued coefficients? -Possible? - If so, how? And what might it even mean?! - Just pondering. Hm?... - (So, for a start, I'm off to watch your vid on 'Line Integrals over Vector Fields'! :) ...)

[@sashimiPv]

This is just the right amount of nerdy! Love it!

[@fireballman31]

Ridiculously good video. I had been searching for exactly this

[@Kil2503]

THE SCREEN IS TOOO BRIGHTTTT

[@swamihuman9395]

- Well done; great presentation. Thx. - AWESOME, in all dimensions! :)

[@saumitrachakravarty]

I wish I had you as my teacher when I took my calculus courses in school

[@xypheli]

Pain with extra steps; I love it 👍🏼

[@AlbertTheGamer-gk7sn]

Cool! Now, try a flow integral, which is defined as a line integral that involves a path through a vector field, which are usually marked as ∮ F ∙ dr, or ∫(F ∙ t)ds. Also, this is an example of a work integral for a force field. For the same force field, a similar formula exists for the magnitude of torque in a 2D vector field with ∫(F ∙ n)ds.

[@FoolishChemist]

Next video already in the making 🫡

[@Twodoor1]

3:58 double jointed pen grip goes crazy lmao

[@jessejordache1869]

I forget how to do line integrals but I remember they're the conceptually easiest but the biggest pain to actually calculate.

[@actualBIAS]

Love your video style. Keep it up!

[@Nino21370]

The intro was too funny 🤣

[@zidanbokhtiar07]

5:41 , I really love this part !

[@cronos30011]

Great video! It has been a while since I took courses on calculus and this was a great way to refresh my memory. I don't really love infinitesimals lol it would also have been nice to see the proof using limits

[@pedroivog.s.6870]

I wish I had been presented to multivariable functions during High-School

[@mmdejong403]

I think the basic line integral is a weighted sum of infinitesimal vectors. The result is again a vector. Taking the length of ds complicates matters, and generates a big discrepancy with line integrals in the complex analysis.

[@anilchoudhary6155]

That HDR effect😂 shined through my eyes

[@authorttaelias4483]

This is so easy to understand!!!

[@alejrandom6592]

I just skimmed through the video but I think ur good at explaining stuff 😊

[@HamzaAli-hh7ub]

you just earned a subscriber dear friend

[@caioesteves1520]

amazing video! what’s that app you used to write in your ipad??

[@FoolishChemist]

Penbook!

[@danmiller9834]

Please make a video on surface integrals next!!! I love the way you explain

[@AJ-et3vf]

Awesome video! Thank you!!!

[@GentlemensShorts]

Great video keep it up man

[@AlexTheGranner]

I love multivariable calculus!

[@antoniocicchella7574]

What app do you use for your notes? However, good and clear video!

[@FoolishChemist]

Pen book on iPad!

[@antoniocicchella7574]

@@FoolishChemist Thank you!

[@rwharrington87]

Officially new favorite channel. Wide Putin 😂

[@JaimeBeilis]

incredible explanation.

[@ازادي-ث5ع]

The master ..BIg Thanks .

[@EhsanulKarim-dn9fb]

Bro you rocked

from Morocco thank you very much

[@josephtennyson4188]

this guy is good

[@-VinhKhang_yearsago]

You deserve more views 👏

[@kareemfareed8486]

Can u make a video for the surface integral 😇😇 , Great work btw

[@silverwoodchuck47]

7:10 mind blown.

[@isaacgaleao]

ikr???

[@Pedritox0953]

Common math's student experience as usual

[@benceleventeode9898]

Thanks!!!

[@mnqobimsizi4328]

Bro use the scaler method of S(dQ/dx-dP/dy)D integration limits are 1 to 3 choose x or y direction

[@Duskull666]

Please do path integrals next :)

[@epicchocolate1866]

A path integral is not a distinct thing.

[@Duskull666]

@@epicchocolate1866 you mean Feynman's path integral in quantum field theory is not distinct?

[@ZaeemAhmad785]

Thanks a lot for this intuitive explanation. By the way, would you mind sharing what app you're using to write the notes? It looks really clean. Thanks in advance!

[@FoolishChemist]

Penbook on iPad!

[@可無-v6m]

very helpful！

[@wain___614]

came here to learn about integrals but stayed because i was trapped in a domain expansion!

[@alexandermeriakri3889]

Loved the video thanks!

[@wain___614]

so solving line integrals mostly depends on the chosen methods of parametisation?? Like instead of using t,can we use trigs to parametise??

[@leonardobarrera2816]

dude, you are incridibly awsome person

[@Striderr10]

1:09 maybe it really was that epic!!!

[@ongopom]

underrated

[@Player_is_I]

Love ur vids❤

[@mintusaren895]

Which one to choose itegral or differential.

[@189thasinahmed7]

Easy and clear sir,,,,will you please also clear doubts on surface integral and volume integral

[@FoolishChemist]

Will do! Those are coming up soon ✍

[@sinewaveaddict]

Such a good video 😂

[@martinluther3712]

Hello, someone say me which software have used in the video to write the mathematical expressions?

[@2kreskimatmy]

this is cool

[@rudransh118]

thanks bro

[@erahamzah6983]

Bro gimme that music at the domain expansion

[@ParasJee-jc3zm]

Genius.

[@JoyaRaniModakChowdhury]

bro😍🤩

[@the_eternal_student]

How did you get ti + t^3j from y=x^3? How is y=x ti+tj and not -ti+tj?

[@willthecat3861]

Thanks for the video. IMO... line integrals over a curve in... for instance R^2 or R^3... are 'busy work" 99% of people... outside math class... needing to do this (and who does?)... They are going to be doing it numerically.

[@FoolishChemist]

Very true! Aside from maybe the arc length formula, I don't think I've never done a line integral of a regular curve in a non-math-class setting. Though I do think thoroughly understanding them is really important for understanding the more practically useful topics ... particularly with line integrals over vector fields

[@Veraliic]

me watching videos abt like integrals when i dont even have practice with the rules for 1D integration👁👄👁

[@the.lemon.linguist]

just curious, when you have f(r(t)) written, does that simply just equal f(x(t),y(t),z(t),…) for all variables involved?

[@FoolishChemist]

Yup, exactly! r(t) is the vector-valued function that contains x(t), y(t), z(t), ... etc as vector components, and the notation says to replace all x's in f(x,y,z) with x(t), all y's with y(t), etc

[@AlbertTheGamer-gk7sn]

@@FoolishChemist There are also vector fields such as F(x, y) = .

[@thesheepgod7]

Multivariable > Malevolent Shrine imo

[@panos21sonic]

Ill be doing these in 3 months approx and im scared shitless tf 😭

[@FoolishChemist]

Don’t be!! It takes some time to understand, but if you really dig deep and try to understand calculus on a fundamental level, it will come much more easily!

[@panos21sonic]

@@FoolishChemist Just want to say youre the goat man. Im kind of in a love hate relationship with math, but clear overviews of concepts always excite me, and the 4 videos of yours ive watched on multivar calc did do just that. Application is what scares me the most but ive got time. Hoping i pass my current calc courses to happily get to them tho 😭

[@gilbertohernandez6315]

Hello, what app do you use for notes?

[@FoolishChemist]

Penbook on iPad!

[@inutamer3658]

To expand the domain wouldn't you need f(x,y) not f(x)?

[@user-mf7li2eb1o]

12:46 i feared youd say parametrisation…

[@SultanInStem-t3i]

This video is incredible. Keep up the good work!

[@pedropiata648]

Why only you can be clear 😭😭

[@RUDRARAKESHKUMARGOHIL]

Bam ! Great work bro but I have a doubt what does line integral refers to ? Like integral in single variable refers to area under curve and 2D ones refer to volume what does this(line integral) refers to ? and yep they will be different for different curve what is the relation among them for all the curves ?

[@FoolishChemist]

Great question! Line integrals for 3D functions still refer to areas under a curve, except now image the curve is squiggly instead of straight. I mention that briefly around 10:15 in the video, and I think the image there is very helpful. In dimensions higher than 3D (>2 input variables), you need 4+ dimensions to graph your inputs vs your output, so it's hard to visualize line integrals at this level ... I would say the relationship between all line integrals, regardless of the curve, is that they are all just infinite sums of function outputs taken over 1D shapes (lines), as opposed to higher-dimensional integrals like surface or volume integrals which are taken over 2D or 3D shapes.

[@RUDRARAKESHKUMARGOHIL]

​@@FoolishChemist ty ❤ I also took multivariable class watched,trefor bazzet but still was not able to recall this 😂 I think now I will be able to recall "domain expansion " 😊 good job...you should have choose maths instead of chemistry 😅

[@nicolasandreas1563]

But what do we do in a case with F à vector field?

[@antoniocicchella7574]

You should define a versor tangent to the integration line, namely, for example, tau hat, and define d\vec{s}=ds • \hat{\tau} and in the integral you would integrate the scalar product of the field and this vectorial displacement

[@matulawa2320]

nah bro, new sub

[@maxvangulik1988]

david schwimmer looks so young here

[@FoolishChemist]

Haven't gotten this one before but thanks! 😊

[@Nate-r3f]

The function x^2 + y^2 would be f(x,y), not f(x).

[@johnyeap7133]

clutch 9:30 onwards

[@AlperenBozkurt-tx2bx]

Dunning Kruger 😂

[@Player_is_I]

0:33 That hurt me 😢

[@dienosorpo]

Bro precalculus is a different thing from multivariable calculus what u on?? You do not see f(x,y) in highschool bro

[@FoolishChemist]

Seems the Mandela effect got to me… 😂

[@dienosorpo]

Awesome bro, great vid. Your humor annoyed me tbh, but its s good video

[@Cooososoo]

Nah I'd win😂

[@franciscoreyes7370]

Actually y is just a constant, since your function, f(x), is just a function of one independent variable x.

[@Abhishek-bz5is]

u cooked

[@elhominid4597]

GAS

[@ionmeriniuc169]

You kinda lost me after the minute 16:00 got too hard

[@gyanprakashraj4062]

😂😂😂😂THESE SHOW UR LEVEL....FIRST THEOREM...ACTUAL MATH KAA AISA HII HOTA😂😂

[@kou-u2o]

😂

[@kLJiga]

Too much circus. I understand, you are very young, but a lot of time is spent on exhibitions.

[@piotr1175]

Boomer detected, opinion rejected

[@faraday4048]

just a clown