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
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!
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.
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.
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.
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.
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..............................
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 !
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
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.
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
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?
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!
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.
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!
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!
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.
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
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.
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 ?
*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.*
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
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.
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
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.
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?
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
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
I'm so glad I can help! :D
@@kristakingmath you are the best mam
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!
So true.....
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.
Final in 2 hours, the best Stoke Theorem video on UA-cam! Thanks krista!
You and professor leonard should start a league of justice
ohh yeahhh!
I really really want at least one of them to do a series on differential forms!
Lol 🤣
😂😂
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.
Awww that's awesome! I'm so glad it helped! :D
I love these more advanced topics on your channel, Krista!
Thanks for the feedback!
I don't like this video because fast
rgvfan video still fine with video speed 1.25 ...
What do you mean more advanced? Coz I'm doing this in grade 5 I'm 11 years old
@@Robertianocockrell seriously? where do you study?
i miss the old days when i thought triple integrals were a lot
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
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.
Not gonna lie but this lady has advanced me from my year1-3 engineering degree, thanks Krista
Hi Krista. Love your channel. Super happy that you have done a more advanced video. Would love to see more :)
Thanks. :)
This is the best video i've ever watched about stokes' theorem. Lots of thanks.
Thanks, Cem! I'm so glad you liked it! :D
I wish i saw ur videos at the beginning of the semester i love u so much bruh
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
Good luck on the final! :D
Congrats on 200k Krista!
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.
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..............................
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 !
Honestly the cool thing about Stokes theorem is your explanation, thanks a lot.
Glad you liked it!
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
So glad it could help! 😀
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.
Thank you!!!! Life saver!! finals are in two days and i finally inderstood it
Watched a lot of videos about this topic( and it didnt quite help) but now, I fully understand because of your lecture. Thank you!
That's awesome! So glad it could help. :)
Loved the way you presented this concept, thanks a LOT
Final is in 5 hours lmao thanks for saving me =D
Hope it went well!
Im in the same boat lmao
Mine's tomorrow boiiiiiiiiiiiiiiii
Mine's tomorrow. so ducked
mine is in 8 hr!!!!!!!!!
Posted right after my final...
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
thank you for making this so much more intuitive
Thanks krista , love from india .....
Great video but you didn't explain why we suddenly get negative P and negative Q at 14:31? (but still positive R)
Thanks Krista, I have really enjoyed watching your videos.
I'm so glad, Mustafa! :)
so simply explained. thanks krista
this video is so amazing im gatekeeping this from my class
thank you so much!!!! i had no idea why my prof kept doing different things. your video cleared things up for me
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 ?
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?
Thank you! The video is very well explained and useful!
Glad it helped, Maxime! :D
I swear to god I just wanna ask you to do stokes theorem .. you are my hero krista, thanks !!
:D
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!
Calc 3 final this morning. Thanks for the brain warm up. Awesome video.
Hope it went well!
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?
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
please explain verify part of 10:19 . How to solve LHS curlf.n.ds
literally math ASMR
14:20 I dont understand anything after this..Why like this? Why take g like this? How are both equal?
I think you use the same textbook I use for class I love your examples and how clear you make everything to understand!!
What's the name of the text book
Why did you took dg/dx and dg/dy? what's the logic behind it?
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.
I wish she would have explained this too.
@@ivangushkov3651 which two vectors are you talking about?
@@jadel.8450 long story. Doesnt really matter. Just use it :)
@@ivangushkov3651 But don't we need to normalise the unit vector by dividing with magnitude?
This is exactly what I needed thank you
*chef's kiss*
here to say this video was so very much appreciated in the ... questionable year of 2019.
Huh? What's so questionable? I'm positive it's still 2019 (for a few more weeks at least), and mathematics still works.
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!
Thank you Krista.. Good balance of broader context and required focus....
That was unbelievable ❤
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.
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?
would love to learn more from your videos , again can't say anything else but THANK YOU, have really been hepled
Aw thanks Alvin! Glad I've been able to help.
This is amazing, thank you so much! At last this makes sense to me
You're so welcome, I'm glad it helped! :D
thanks for helping me graduate uni!!
In example 2, why is it negative p and q but positive r?
omg u saved my life my calc III final is in an hour thank youuuuu
Glad it helped, and hope the Calc III final went GREAT! :D
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?
18:40 I got -pi/2 when i switch to polar coordinates. Is that correct?
The explanation is awesoms
Many thanks to you Krista King
I'm happy to help! :)
I've finally understood this. THANK YOU!
Awesome video! Thank you.
On the second example when calculating the CURL why do you subtract the j matrix? The formula is supposed to add all 3 matrix
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!
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.
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.
Your video is so awesome! I get this now. Thanks a lot!
This is perfect timing, I have a final tomorrow with Stokes on it.
Good luck on the final!
Thank you Krista!
You're welcome! Glad it could help.
Online lectures: Following lecture => Confusion => UA-cam math channels => Enlightenment
Great video! Please tell me the app that you use to write in the video, it’s useful for teaching online. Many thanks!
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
This is actually a significantly better explanation of this topic than what Khan academy provided
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
this is way different than what i have learnt in class...confused. why in 1.example u didnt find ds?
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.
this is so helpful for me Krista King
Awesome! Thanks for letting me know.
Krista King
Great video! I wish you also had one on the Divergence Theorem.
I have one already in my school that I just haven't published to UA-cam. Hopefully soon!
Had my Calc 3 final last night!! Anyways, thanks for making all the videos. They have really helped me a lot!
You're welcome, and congratulations on being DONE!!! :D
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 ?
where's the normal vector in the formula?
Finals in three days ! Thank You!!
all doubts cleared thanks :)
this was a very helpful and education video!
Thanks! I'm so glad it helped! :)
All thanks to YOUR videos Krista ***
So glad they're helping Alvin!
Thanks krista
Iove from IRAQ :)
Thank you, this really helped
why is it not integral curl F (dot) N dS??anyone helpppp it’s confusing me with surface intergral
*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.*
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
Isaac T. It seems you found Google after all
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.
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
I do have a video on divergence theorem that I'll hopefully be able to publish soon. :)
Amazing video !!!
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.
No one cares
I am a math tutor with a child who is in engineering. I watch your videos and use those to teach my child
Krista King you are awesome
Thank you very much. Your video helped me a lot.
You're welcome!
can you use stokes' thm on rectangles since they aren't smooth?
yes, piece-wise smooth, break em up into 4 separate lines that are smooth, do the integral thing, and add em together
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?
Thank you, this helped me master stokes theorem
Awesome! Glad it could help.
Awesome efforts thank you! (India)
You're so welcome! Glad I can help.
I have little confusion at "14:42" why P and Q are negative? can you please tell?
Thank you in advance
What book do you use?
I love this Lecture i really want to more video which helps us ..........however THANK YOU
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
Thanks for making us understanding easily. 😊
:D