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 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'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 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.
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 !
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
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.
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.
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
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.
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?
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.
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!
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!
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.
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
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
*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.
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
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 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'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.....
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
Final in 2 hours, the best Stoke Theorem video on TH-cam! Thanks krista!
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.
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?
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.
Thanks, Cem! I'm so glad you liked it! :D
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..............................
Hi Krista. Love your channel. Super happy that you have done a more advanced video. Would love to see more :)
Thanks. :)
Thank you!!!! Life saver!! finals are in two days and i finally inderstood it
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!!!!!!!!!
Honestly the cool thing about Stokes theorem is your explanation, thanks a lot.
Glad you liked it!
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 !
Loved the way you presented this concept, thanks a LOT
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
I wish i saw ur videos at the beginning of the semester i love u so much bruh
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. :)
Posted right after my final...
thank you for making this so much more intuitive
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.
Congrats on 200k Krista!
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
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 so much!!!! i had no idea why my prof kept doing different things. your video cleared things up for me
Thanks krista , love from india .....
this video is so amazing im gatekeeping this from my class
Thank you! The video is very well explained and useful!
Glad it helped, Maxime! :D
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! 😀
literally math ASMR
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!
Thanks Krista, I have really enjoyed watching your videos.
I'm so glad, Mustafa! :)
Great video but you didn't explain why we suddenly get negative P and negative Q at 14:31? (but still positive R)
so simply explained. thanks krista
Calc 3 final this morning. Thanks for the brain warm up. Awesome video.
Hope it went well!
This is exactly what I needed thank you
thanks for helping me graduate uni!!
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?
I swear to god I just wanna ask you to do stokes theorem .. you are my hero krista, thanks !!
:D
I've finally understood this. THANK YOU!
This is amazing, thank you so much! At last this makes sense to me
You're so welcome, I'm glad it helped! :D
Finals in three days ! Thank You!!
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
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
This is perfect timing, I have a final tomorrow with Stokes on it.
Good luck on the final!
Many thanks to you Krista King
I'm happy to help! :)
The explanation is awesoms
All thanks to YOUR videos Krista ***
So glad they're helping Alvin!
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?
all doubts cleared thanks :)
Thank you Krista!
You're welcome! Glad it could help.
Awesome video! Thank you.
Krista King you are awesome
Thank you, this helped me master stokes theorem
Awesome! Glad it could help.
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 actually a significantly better explanation of this topic than what Khan academy provided
this is so helpful for me Krista King
Awesome! Thanks for letting me know.
Krista King
Online lectures: Following lecture => Confusion => TH-cam math channels => Enlightenment
Your video is so awesome! I get this now. Thanks a lot!
I am a math tutor with a child who is in engineering. I watch your videos and use those to teach my child
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.
Thank you, this really helped
That was really helpful
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.
I'm .................................................Stoked ~
🤓
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.
this was a very helpful and education video!
Thanks! I'm so glad it helped! :)
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....
Thank you very much. Your video helped me a lot.
You're welcome!
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.
Thanks a lot! Finally understood!
:D
I love this Lecture i really want to more video which helps us ..........however 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.
Great video! Please tell me the app that you use to write in the video, it’s useful for teaching online. Many thanks!
Thanks krista
Iove from IRAQ :)
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?
Amazing video !!!
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
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
You're the best!!
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. :)
Thanks for making us understanding easily. 😊
:D
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 was very helpful thank you!
You're welcome, Simone! I'm so glad it helped! :D
Very cool
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 TH-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
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
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?
On the second example when calculating the CURL why do you subtract the j matrix? The formula is supposed to add all 3 matrix
*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.
love you @Krista King that was awesome
Thank you so much!
Hello Krista, thanks for the video. Is surface S limited by curve C arbitrary chosen?
Thank you, you’re awesome
thnks a lot krista!!!!!!!
😊
wise woman with a beautiful voice.
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