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.

[@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.....

[@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

[@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]

😂😂

[@aojiao2823]

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

[@pipturbine473]

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

[@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.

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

[@mohammeda4116]

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

[@kristakingmath]

Glad you liked it!

[@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..............................

[@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.

[@IMadeOfClay]

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

[@kristakingmath]

Thanks. :)

[@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.

[@Milgamix77]

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

[@andyfox4354]

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

[@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

[@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 !

[@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!!!!!!!!!

[@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

[@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.

[@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

[@cooperlane7147]

Congrats on 200k Krista!

[@harshitsinghai1395]

Thanks krista , love from india .....

[@Mada1100]

Posted right after my final...

[@osamaalmansari]

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

[@kristakingmath]

:D

[@DavidPumpernickel]

thank you for making this so much more intuitive

[@pinkybananas1]

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

[@JumpinJellyBeansA]

this video is so amazing im gatekeeping this from my class

[@MAXTHEREMIX]

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

[@kristakingmath]

Glad it helped, Maxime! :D

[@mustafaomar7448]

Thanks Krista, I have really enjoyed watching your videos.

[@kristakingmath]

I'm so glad, Mustafa! :)

[@yurii6080]

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

[@Greg-It]

literally math ASMR

[@asamonson6866]

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

[@kristakingmath]

Hope it went well!

[@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 ?

[@real_john_doe]

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

[@imtiazursyed1521]

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

[@peilin2428]

currently taking civil engineering degree,it's 20 days before FYP of math,i bow to u😭❤U SAVE MY LIFE and MARKS,THANKS GOD

[@kristakingmath]

So glad I can help!! :D

[@FrancisAAfful]

so simply explained. thanks krista

[@lalotothemax]

That was unbelievable ❤

[@DeathCoconut]

thanks for helping me graduate uni!!

[@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!

[@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.

[@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!

[@zarehdarakjian2476]

One of a kind explnation! Great work! Just that, as Kumayun Khawar alerted us to, it would be better to make it very clear that at this point we don't need to worry about where the partial derivatives of "g" all of a sudden appear on the RHS of the flux integral... or may be some explanation as to why that equality could hold at all.... Thank you again, Krista! God bless you!

[@zarehdarakjian2476]

Thank you Krista.. Good balance of broader context and required focus....

[@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

[@maazqamar9567]

The explanation is awesoms

[@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?

[@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

[@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

[@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?

[@BBitIT]

This is exactly what I needed thank you

[@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

[@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.

[@naomiaguilar685]

I've finally understood this. THANK YOU!

[@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! :)

[@abdelz1617]

Awesome video! Thank you.

[@A58i2]

All thanks to YOUR videos Krista ***

[@kristakingmath]

So glad they're helping Alvin!

[@jedhe2695]

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

[@obsidiantechz1371]

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

[@2000pml]

Finals in three days ! Thank You!!

[@gaaraofddarkness]

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

[@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!

[@mohammedmuala7087]

Thanks krista Iove from IRAQ :)

[@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.

[@tinanashe8814]

Krista King you are awesome

[@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?

[@usmanraoof6]

this is so helpful for me Krista King

[@kristakingmath]

Awesome! Thanks for letting me know.

[@saivenkatdurgaprasad2117]

Krista King

[@samseuropejourneys838]

all doubts cleared thanks :)

[@hchannel4425]

Thank you, this really helped

[@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.

[@peacefulasmr8351]

You're the best!!

[@EsperanceBG]

Thank you Krista!

[@kristakingmath]

You're welcome! Glad it could help.

[@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?

[@narnar707]

this was a very helpful and education video!

[@kristakingmath]

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

[@jadel.8450]

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

[@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

[@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

[@akshaythakur262]

Awesome efforts thank you! (India)

[@kristakingmath]

You're so welcome! Glad I can help.

[@akshaythakur262]

I have little confusion at "14:42" why P and Q are negative? can you please tell? Thank you in advance

[@julianarrieta3125]

Amazing video !!!

[@360-t5s]

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

[@katherine4386]

Thank you, this helped me master stokes theorem

[@kristakingmath]

Awesome! Glad it could help.

[@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?

[@buddydog1956]

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

[@kristakingmath]

🤓

[@bu3b00d]

Thank you very much. Your video helped me a lot.

[@kristakingmath]

You're welcome!

[@Dra60oN]

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

[@martinperu6207]

What book do you use?

[@neilsarma4722]

Thanks for making us understanding easily. 😊

[@kristakingmath]

:D

[@bhaveshohal3390]

That was really helpful

[@thecornydocc]

I love this Lecture i really want to more video which helps us ..........however THANK YOU

[@vithiyananthanesanmanuelje3772]

Awesome 👍👍👍👍👍👍 madam It's Just save my time

[@kristakingmath]

I'm so glad it helped! :)

[@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.

[@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

[@tachrinc7361]

love you @Krista King that was awesome