What is Stokes theorem? - Formula and examples

[@sabdf2877]

Finding videos for math this advanced that is this high quality and well explained is very rare. You and Prof Leonard have saved my calc grades 1-3! Thank you so much! Engineers everywhere bow down to you

[@kristakingmath]

I'm so glad I can help! :D

[@tichaonamarariromba4838]

​@@kristakingmath you are the best mam

[@leslypaz5094]

I've spent the last two hours watching KHAN videos and looking up other videos/pdf on Stokes Theorem. I somehow came across your video, and I completely understand it now. You teaching method is superb and at good pace, and you just saved my life because my test is tomorrow.

[@tb4243]

I was in tears over Stokes Theorem...I didn't understand what was going on at all. Twenty minutes with you and I'm out of the dark. I can't tell you how grateful I am.

[@kristakingmath]

Awww that's awesome! I'm so glad it helped! :D

[@grum4205]

I've been trying to learn Stokes Theorem through Khan Academy, and your video is so much more comprehensible then their entire collection of videos on the subject. Thanks so much!

[@saqibshams5143]

So true.....

[@omars_projects]

You and professor leonard should start a league of justice

[@CCAPACCO]

ohh yeahhh!

[@joefuentes2977]

I really really want at least one of them to do a series on differential forms!

[@sekhar018]

Lol 🤣

[@shivangsingh5834]

😂😂

[@neemo9885]

i miss the old days when i thought triple integrals were a lot

[@DavidPumpernickel]

Yeah oh my god... It's been two months since I've taken vector calculus and I miss how easy it was in hindsight xD

[@joefuentes2977]

Line integrals for curves, surface integrals for surfaces, triple integrals for volume, and quadruple integrals for space-time continuum a.k.a. the end of the world.

[@aojiao2823]

Final in 2 hours, the best Stoke Theorem video on KZbin! Thanks krista!

[@picknikbasket]

I love these more advanced topics on your channel, Krista!

[@kristakingmath]

Thanks for the feedback!

[@rgvfan7098]

I don't like this video because fast

[@bbergspitze]

rgvfan video still fine with video speed 1.25 ...

[@Robertianocockrell]

What do you mean more advanced? Coz I'm doing this in grade 5 I'm 11 years old

[@saifashraf8474]

@@Robertianocockrell seriously? where do you study?

[@pipturbine473]

Not gonna lie but this lady has advanced me from my year1-3 engineering degree, thanks Krista

This is the best video i've ever watched about stokes' theorem. Lots of thanks.

[@kristakingmath]

Thanks, Cem! I'm so glad you liked it! :D

[@Anmolorb]

Final is in 5 hours lmao thanks for saving me =D

[@kristakingmath]

Hope it went well!

[@qilongli]

Im in the same boat lmao

[@Jack-cm5ch]

Mine's tomorrow boiiiiiiiiiiiiiiii

[@jacobgomez_]

Mine's tomorrow. so ducked

[@yifan863]

mine is in 8 hr!!!!!!!!!

[@cooperlane7147]

Congrats on 200k Krista!

[@A58i2]

thank you sooooo verrry much, great success attended me during my MATH exam last semester................ all thanks to videos through which I studied successfully................................... you've been a blessing to people like me..............................

[@trendytrenessh462]

Great video but you didn't explain why we suddenly get negative P and negative Q at 14:31? (but still positive R)

[@IMadeOfClay]

Hi Krista. Love your channel. Super happy that you have done a more advanced video. Would love to see more :)

[@kristakingmath]

Thanks. :)

[@mohammeda4116]

Honestly the cool thing about Stokes theorem is your explanation, thanks a lot.

[@kristakingmath]

Glad you liked it!

[@Milgamix77]

I wish i saw ur videos at the beginning of the semester i love u so much bruh

[@timothyobaob3624]

At 5:07, let's say that it wasn't necessarily bound by z=0, but rather some positive constant, let's say 1. would that change the r(t) function to ?

[@humayun007]

Why did you took dg/dx and dg/dy? what's the logic behind it?

[@ivangushkov3651]

The logic behind it, is that dS is NdA, where N is a normal vector given as (-dz/dx, -dz/dy, 1) (this comes from a cross product between two other vectors, but don´t worry about it just use it). When you dot the curl with that normal vector you get the answer she showed, it´s just that she skipped over that step.

[@corey333p]

I wish she would have explained this too.

[@jadel.8450]

@@ivangushkov3651 which two vectors are you talking about?

[@ivangushkov3651]

@@jadel.8450 long story. Doesnt really matter. Just use it :)

[@dominicj7977]

@@ivangushkov3651 But don't we need to normalise the unit vector by dividing with magnitude?

[@andyfox4354]

Thank you!!!! Life saver!! finals are in two days and i finally inderstood it

[@IaKhanic]

Also how would you solve it if at the end things don't cancel out? For example, if you were left with, Double integral of 2x da does it become integral from 0-1 integral from 0-1 2x dy dx like the first one?

[@Mada1100]

Posted right after my final...

[@MadMagzzz]

How would you visually interpret a negative area? Or does the sign matter at all to what it means visually? Thank you so much for all the amazing videos!

[@muwongeevanspaul9166]

Lady Krista thanks alot but truthfully,its a tough battle to understand; better to admit. Honestly,it requires u do for us more worked examples but above all,thanks alot so much.

[@josecarlosribeiro3628]

Hi Krista! Your classes are beautiful! Congratulations for you ability and competence! I learning a lot with you! Thank and my neste regards! José Carlos- Jacareí - São Paulo-Brazil.

[@JumpinJellyBeansA]

this video is so amazing im gatekeeping this from my class

[@Sstratos94]

You have done a very good job! I really hope to continue the great work . I work with math like this almost every day and the only thing that I want to say is that the way that you present it is really wonderful. Good job !

[@FrancisAAfful]

so simply explained. thanks krista

[@DavidPumpernickel]

thank you for making this so much more intuitive

[@MAXTHEREMIX]

Thank you! The video is very well explained and useful!

[@kristakingmath]

Glad it helped, Maxime! :D

[@harshitsinghai1395]

Thanks krista , love from india .....

[@gtowaru]

you saved me!!!! i was having trouble understanding what the heck C is the boundary of S meant when trying to do my homework and this really helped me get it! thank you so much! :D

[@kristakingmath]

So glad it could help! 😀

[@A58i2]

Loved the way you presented this concept, thanks a LOT

[@europeankid98]

So at 18:20, are we trying to get the double integral in sole terms of dA? And if we can't, would we just integrate with dx and dy like usual?

[@360-t5s]

I was thinking the same case with x going from 0 to 1 and the same for y->0 to 1. but i end up with -2 not -1

[@ruffinist]

Krista the KING FTW just in time for my final tomorrow!!! Dude, you are literally saving me, this was the one thing i was having trouble with

[@kristakingmath]

Good luck on the final! :D

[@Greg-It]

literally math ASMR

[@obsidiantechz1371]

please explain verify part of 10:19 . How to solve LHS curlf.n.ds

[@hannahjoyceliz5821]

Watched a lot of videos about this topic( and it didnt quite help) but now, I fully understand because of your lecture. Thank you!

[@kristakingmath]

That's awesome! So glad it could help. :)

[@victorpaesplinio2865]

Thank you for the clearest explanations! In the second example I solved for the other side (line integral) and it matched! I think that now I can nail my last calc 3 exam for the semester

[@osamaalmansari]

I swear to god I just wanna ask you to do stokes theorem .. you are my hero krista, thanks !!

[@kristakingmath]

:D

[@mustafaomar7448]

Thanks Krista, I have really enjoyed watching your videos.

[@kristakingmath]

I'm so glad, Mustafa! :)

[@chasemckinley2]

Extremely helpful video. I'm still a bit unclear as to the curl of F dotted with ds being written as -Pdg/dx-Qdg/dy+R...Does that always apply when calculating a dot product between ds and curl F? Either way the video gave MUCH needed insight that several other sources seemed to lack for me so THANK YOU!

[@briandwi2504]

Yes, I didn't like that part either. It wasn't clear what was going on. Best keep it as the dot product as you suggest.

[@smrtfasizmu6161]

How did she get from (Pi + Qj + Rk) dS to the -P(dg/dx)-Q(dg/dy) + RdA What's that formula and how can I derive it?

[@gaaraofddarkness]

14:20 I dont understand anything after this..Why like this? Why take g like this? How are both equal?

[@IaKhanic]

This may be dumb, but at 14:23 how did you get that? I understand that you found Curl of F but where did you get the ds from? thanks :P

[@mahtabm8611]

in the 2nd example, why did you choose the shadow of the surface on the xy plane? Is the transformation from surface S to D valid in every question?

[@victorcarvalho2758]

On the second example when calculating the CURL why do you subtract the j matrix? The formula is supposed to add all 3 matrix

[@jadel.8450]

In example 2, why is it negative p and q but positive r?

[@NhanLe-lg7sg]

Great video! Please tell me the app that you use to write in the video, it’s useful for teaching online. Many thanks!

[@Calculus58]

By looking at their graphs you can tell that integrating functions such as sint, sin2t, cost and cos2t between t = 0 and 2pi will give an answer of 0.

[@acd4807]

this is way different than what i have learnt in class...confused. why in 1.example u didnt find ds?

[@ivangushkov3651]

In the first example you don´t need to find dS, as you are going the other way around with the theorem. When you go the other way around and parametrize the circle you get to integrate with respect to the parameter anyway. In the second example, if you go the "usual" way with the theorem, you actually have to evaluate dS, which is NdA, where N is a normal vector to the surface S. You get that normal vector as (-dz/dx, -dz/dy, 1) and you dot the curl with it.

[@janetm519]

*chef's kiss* here to say this video was so very much appreciated in the ... questionable year of 2019.

[@Jeremy_Fisher]

Huh? What's so questionable? I'm positive it's still 2019 (for a few more weeks at least), and mathematics still works.

[@ulisesfalmonte2496]

when do we use -P(dG/dX)-Q(dG/dX)+K dA? is it when we have to use the shadow of the plane onto the xy-plane, because dA represents a flat surface? can we also use it to find cult F*dS ?

[@ivornworrell]

*Krista you're erudite in mathematics & your explanations are pellucid, but can you pls tell me how Stokes is applicable to the real world, or is it just brain exercise?Thanks.*

[@isaact.477]

Measuring circulation of a fluid (gas, liquid) over a closed region that can be bounded by a parameterized curve. Measuring how much water flows through a net/barrier per unit time

[@197jm]

Isaac T. It seems you found Google after all

[@isaact.477]

If someone is going to post videos on math topics, they should explain the intuition to their viewers and connect it to the written math. If you don't agree with that, you most likely have a weak foundation in mathematics.

[@lalotothemax]

That was unbelievable ❤

[@superuser8636]

Krista, I love ALL your videos, but I don't think your integral is correct at 10:41. I am getting 0 and not -9[2pi]. I can send you my handworked notes as well but I just did double-check on Wolfram. -9 * Integral[1-cos(2pi)]dt = Integral[-9+9cos(2pi)]dt = 0 The reason why will be obvious right away unless I've made a mistake by hand here. EDIT: It just occurred to me! that -9[2pi] = -18pi = 0 Even though I drew it out .... I still prefer 0

[@arshad3491]

Many thanks to you Krista King

[@kristakingmath]

I'm happy to help! :)

[@pinkybananas1]

thank you so much!!!! i had no idea why my prof kept doing different things. your video cleared things up for me

[@yurii6080]

Online lectures: Following lecture => Confusion => KZbin math channels => Enlightenment

[@brydust]

where did you get the relation \int \int_S curl F dS = \int \int_D -P etc.... dA? Is there a name for this relation? Or do you have a video where you explain this?

[@siphilipe]

Sorry, I am not studying for tests or finals, but for knowledge. Could you explain all that practically, what is it exactly?, and in what part in real life we (as future engineers) will face these oriented curve and smooth surface and ... ? Thanks for sharing.

[@BBitIT]

This is exactly what I needed thank you

[@DeathCoconut]

thanks for helping me graduate uni!!

[@maazqamar9567]

The explanation is awesoms

[@360-t5s]

18:40 I got -pi/2 when i switch to polar coordinates. Is that correct?

[@bhgomes]

Suggestion: You should use arrows and hats to indicate vectors. For example: 'dS' is as a vector because the flux is always calculated in the normal direction. In the video, you didn't use the symbol, not even wrote the 'n' vector in the formula. For those who are still learning, it can be messy to understand. Surely dot/cross products occur only between vectors, but doing this will emphasize some concepts and help to connect with other references.

[@FunkySoulBandit]

No one cares

[@Dra60oN]

Hello Krista, thanks for the video. Is surface S limited by curve C arbitrary chosen?

[@EsperanceBG]

Thank you Krista!

[@kristakingmath]

You're welcome! Glad it could help.

[@2000pml]

Finals in three days ! Thank You!!

[@asamonson6866]

Calc 3 final this morning. Thanks for the brain warm up. Awesome video.

[@kristakingmath]

Hope it went well!

[@collegestudent6071]

I just don't understand where that partials setup came from when you were setting up the integral.

[@cykoshadow]

The first equation you have is double integral over S of curl F dot dS. When the surface is given by an equation of z = f(x,y), you are able to use the equation over D with the partials that she used. It’s a special case, may not have been covered by your professor.

[@mdanialmk9786]

why is it not integral curl F (dot) N dS??anyone helpppp it’s confusing me with surface intergral

[@steazemcgheaze7540]

can you use stokes' thm on rectangles since they aren't smooth?

[@ruffinist]

yes, piece-wise smooth, break em up into 4 separate lines that are smooth, do the integral thing, and add em together

[@imtiazursyed1521]

I am a math tutor with a child who is in engineering. I watch your videos and use those to teach my child

[@A58i2]

All thanks to YOUR videos Krista ***

[@kristakingmath]

So glad they're helping Alvin!

[@SofiaSkywalker]

This is amazing, thank you so much! At last this makes sense to me

[@kristakingmath]

You're so welcome, I'm glad it helped! :D

[@brooklynwright7109]

where's the normal vector in the formula?

[@nnass262]

Thanks for the great explanation, you have all my respect this seems easy as hell copared to the mess we learned. Aren't we supposed to use Ds in stokes theorem like DSx= (dy dz ) i when working on the right side

[@abdelz1617]

Awesome video! Thank you.

[@usmanraoof6]

this is so helpful for me Krista King

[@kristakingmath]

Awesome! Thanks for letting me know.

[@saivenkatdurgaprasad2117]

Krista King

[@martinperu6207]

What book do you use?

[@melissaY63]

I think you use the same textbook I use for class I love your examples and how clear you make everything to understand!!

[@lynettebirir7007]

What's the name of the text book

[@rickrocks3000]

This is perfect timing, I have a final tomorrow with Stokes on it.

[@kristakingmath]

Good luck on the final!

[@mathlover2299]

Do you have any diff EQ material? If not do you have a good source? KZbin or otherwise? PS you def helped me get straight A's though Calc and for that I am very thankful (never had a test less than 95% because of all the examples you have)

[@kristakingmath]

Awesome, I'm so glad I was able to help! I have some DE stuff, here: kzbin.info/aero/PLJ8OrXpbC-BO2zEW58TpHHakh5nodn3-i It's not a complete course, but maybe some of the videos in there will be helpful. :D

[@real_john_doe]

This is actually a significantly better explanation of this topic than what Khan academy provided

[@Caarve]

Great video! I wish you also had one on the Divergence Theorem.

[@kristakingmath]

I have one already in my school that I just haven't published to KZbin. Hopefully soon!

[@Caarve]

Had my Calc 3 final last night!! Anyways, thanks for making all the videos. They have really helped me a lot!

[@kristakingmath]

You're welcome, and congratulations on being DONE!!! :D

[@juanjoserojas2788]

your videos are amazing !! have you thought on doing one about gauss theorem?

[@aydudie]

omg u saved my life my calc III final is in an hour thank youuuuu

[@kristakingmath]

Glad it helped, and hope the Calc III final went GREAT! :D

[@HoangTran-qw6zx]

When I look up wiki and any other source, your curl of F formula is different, yours is i-j+k while other sources is i+j+k, sorry for my bad english, please confirm?

[@hchannel4425]

Thank you, this really helped

[@jedhe2695]

Your video is so awesome! I get this now. Thanks a lot!

[@tinanashe8814]

Krista King you are awesome

[@katherine4386]

Thank you, this helped me master stokes theorem

[@kristakingmath]

Awesome! Glad it could help.

[@buddydog1956]

I'm .................................................Stoked ~

[@kristakingmath]

🤓

[@A58i2]

would love to learn more from your videos , again can't say anything else but THANK YOU, have really been hepled

[@kristakingmath]

Aw thanks Alvin! Glad I've been able to help.

[@narnar707]

this was a very helpful and education video!

[@kristakingmath]

Thanks! I'm so glad it helped! :)

[@mcgarettsteve9077]

keep the videos coming..really amazing stuff and clear explanatory i would like to request if u could do a video on gauss divergence theorem as well if u have the time for it..thank you..thanks for the video and appreciate the effort

[@kristakingmath]

I do have a video on divergence theorem that I'll hopefully be able to publish soon. :)

[@yellowflashgaming9237]

Which software u using to draw

[@kristakingmath]

It's called Sketchbook. :)

[@samseuropejourneys838]

all doubts cleared thanks :)

[@joefuentes2977]

Do a series on differential forms!!!! :D