My dude you are an absolute legend!!! You successfully explained this so much more succinctly and clearly than my textbook ever did. That color coding really helps too! Thank you!!!
Another easier way to test if a vector field is conservative is by finding the curl of the vector field, if the curl is a zero vector(i.e then the vector field is conservative, The curl will automatically check for all the cases that you have listed.
I know this is my second comment on this video, second time going through it, but it's just so beautiful! I remember when I first learned about vector functions and thoughts "Holy shit, there is so much potential here." Well, now I'm seeing some of that potential coming through and I'm loving it
i like your videos for getting an overall understanding of the concept however i think it would be helpful if you went over an example in the same video.
I absolutely love your work, but something that I believe is missing is the fact that using Clairaut's does not always correctly tell us whether a vector field is conservative or not as it does not account for singularities.
this is awesome. in our vector analysis class, we sought grad x gradf = 0, which makes sense analytically since the curl of a gradient is zero, but i don't fully understand this geometrically -- YET!
Dr. Bazett, first of all, thank you for the great video. I would like to ask you a question about this test you are presenting. I believe this "if and only if" property is called the Poincaré-Lemma, where it is stated that it applies only when the domain of F star shaped is (Star Domain), which in general any higher dimension R is. However, we might not be working with a star domain, for example F might be defined on R^2\{0}. In that case, can we still use this test or is it invalid? Thank you in advance!
OMG. This question is exactly what I was thinking when I studied this topic last night. Thank you for writing here. Are you also a mathematics student or just asking out of curiosity?
could you theoretically also test if it's conservative by taking the partial derivative of M w.r.t y, then doing it again w.r.t. z, and testing if it's equal to the expression you get if you do so with N (w.r.t. x and then w.r.t. z) and if you do so with P (w.r.t. x and then w.r.t. y)?
Hi, doctor. What could happen in higher dimensions, like 4, 5, and so on. How could I know if a function is conservative when it is in a dimension higher than 3?
The same basic idea. You need to compare all the possible ways you take the partial of the ith component with respect to the jth variable to the partial with j and i reversed. If all of those match up, it is conservative.
Imagine the curve is a figure 8, and you are driving around and pointing your normal out the window to the left. Sometimes you are pointing INSIDE the curve, sometimes OUTSIDE. That's a problem for measuring the flux via the degre to which it is only going outside. SImply connected blocks that problem.
This kind of math speak is exactly why I hate pure math. Nobody ever explains concepts in words anymore. It's all these weird symbols and logic statements that humans aren't meant to understand. At least engineering has intuitive diagrams and they actually tell you what youre looking for. Anyways, I'm so glad that this is going to be my last semester of dealing with this BS. Thanks for the video, it helped.
![Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]](http://i.ytimg.com/vi/lKXW7DRyyro/mqdefault.jpg)
My dude you are an absolute legend!!! You successfully explained this so much more succinctly and clearly than my textbook ever did. That color coding really helps too! Thank you!!!
Awesome, been looking for this all night!
Thank you so much!!
I was tasked to discuss on line integral and path independent. And I'm so thankful of your videos because I really understood it.
Finally after scrolling through many videos, my need was fulfilled. I finally learnt how to check for conservative fields.❤
Perfect math professor that any students could only wish of. Hats off.
Prof, you're SO good at teaching
I appreciate that!
Another easier way to test if a vector field is conservative is by finding the curl of the vector field, if the curl is a zero vector(i.e then the vector field is conservative, The curl will automatically check for all the cases that you have listed.
How do you check if a 4-dimensional vector field is conservative, if curl only works for up to 3-dimensional fields?
@@carultch use 4 dimensional curl
Thanks a bunch
if i wanted to know if a vector field was conservative i'd just ask them if they voted for trump or biden
Haha, did I really release this vid right after an election, oops😂
Bruh lol
Lol, somehow - to America's great shame - this joke is still relevant in 2024; and in point of fact, it's aged better than the candidates!
I know this is my second comment on this video, second time going through it, but it's just so beautiful! I remember when I first learned about vector functions and thoughts "Holy shit, there is so much potential here." Well, now I'm seeing some of that potential coming through and I'm loving it
Thank you so much for this great content... very concise and straight to the point... You've earned yourself a new subscriber 🙏🙏🙏
You ask the victor field if it wants to raise taxes!🥁🔔😄😎
Lower*
oh ok now I got why the curl of a vector F is equal to the null vector represents path independent
Thank you, Sir 🙏👌
My high school teacher explained that but I couldn't get any grasp thanks for explaining this nicely :)
Great video Dr. Bazett. Thank you very much for doing this.
I can't concentrate on your lecture for your t shirt . All the time I had watched it and try to understand all the figures. 😂😂
lol I love that t shirt so much:D
@@DrTrefor It's amazing 🤩 and I also love this. I need this t shirt 🥺,but not possible I know .
Great , I was just looking for this topic
Thank you for making this video. It’s really helpful.
I HAVE THOMAS AND ITS MY FAVOURITE BOOK . ITS SIMPLY AMAZING . I LOVE IT . FOR REAL ITS PERFECT
Omg this so good, you're the real mvp
Someone's watched a lot of patrickJMT videos :'D
great addition to my lectures thank you
i like your videos for getting an overall understanding of the concept however i think it would be helpful if you went over an example in the same video.
thank you
I absolutely love your work, but something that I believe is missing is the fact that using Clairaut's does not always correctly tell us whether a vector field is conservative or not as it does not account for singularities.
this is awesome. in our vector analysis class, we sought grad x gradf = 0, which makes sense analytically since the curl of a gradient is zero, but i don't fully understand this geometrically -- YET!
Wow! beautiful work sir
Thank you so much!
P, Q, R are often used, instead of M,N ,P . I think M,N is only used for 2d vector fields. tomayto tomahto... great video!
Depends on the text, no standardization here sadly
great video sir i became big fan of you
Thank you so much, and thanks for becoming a member I really appreciate that! :)
Dr. Bazett, first of all, thank you for the great video. I would like to ask you a question about this test you are presenting. I believe this "if and only if" property is called the Poincaré-Lemma, where it is stated that it applies only when the domain of F star shaped is (Star Domain), which in general any higher dimension R is. However, we might not be working with a star domain, for example F might be defined on R^2\{0}. In that case, can we still use this test or is it invalid? Thank you in advance!
OMG. This question is exactly what I was thinking when I studied this topic last night. Thank you for writing here. Are you also a mathematics student or just asking out of curiosity?
@@tnyhwksk8 You know, I am kind of a mathematician myself.
@@ardaozcan98 Kind of?
@@aliemreaksoy1421 I use mathematics to understand, examine and shape nature according to my will.. as much as my budget permits.
@@ardaozcan98 So you are an engineer
Thank you so much sir!
Very helpful video, thank you.
I really like your t-shirt. How can I find it?
could you theoretically also test if it's conservative by taking the partial derivative of M w.r.t y, then doing it again w.r.t. z, and testing if it's equal to the expression you get if you do so with N (w.r.t. x and then w.r.t. z) and if you do so with P (w.r.t. x and then w.r.t. y)?
Hi, doctor. What could happen in higher dimensions, like 4, 5, and so on. How could I know if a function is conservative when it is in a dimension higher than 3?
The same basic idea. You need to compare all the possible ways you take the partial of the ith component with respect to the jth variable to the partial with j and i reversed. If all of those match up, it is conservative.
@@DrTrefor Thanks so much by your answer, greetings from Dominican Republic. 😊😊
VERY VERY HELPFUL , THANK YOU
Sir, can you please explain to me 2:24, I am a newbie in the multivariable calculus.
Can you recommend me a course in order for me to see a proof where partial derivatives commute, I will appreciate.
Nice video, thanks :)
Thank you very much.
You are welcome!
Which video in the calc 3 playlist did you prove the commuting mixed partial trick?
It wasn’t done in a video, sorry, many things get left to my actually classes:/
Why is important that the domain is simply connected? I have never understood this thing.
Imagine the curve is a figure 8, and you are driving around and pointing your normal out the window to the left. Sometimes you are pointing INSIDE the curve, sometimes OUTSIDE. That's a problem for measuring the flux via the degre to which it is only going outside. SImply connected blocks that problem.
Genius.
Thank you very much :)
where did you get your shirt?
Why does the CURL of a force determine if it's conservative of not?
Three vector fields walk into a bar ...
awesome im on this exactly on a year
what happened at 4:11?
hahah oops editing error. If I ever uploaded an uncut version there would be like a hundred of those, I just normally cut them all out:D
Amazing
Thanks.
Thank you!
Thanks for the amazing video professor. I find it funny that the T-shirt had the wrong graph for y=sin(x) :)
ha I suppose it depends where the origin is:D
I think it is better to understand the criterion based on the fact that "grad X grad f = 0".
You are just great
That is a super cool t-shirt👕😂
How does this method differ from the curl method?
No, actually we are going to introduce that in a video a little bit later in the playlist and show they are exactly the same
Simply amazing
Thank you! Cheers!
How do you know if its iff when you have holes ?
🔥🔥🔥
Hello I would like to know where did you get that tshirt from :')
🤭😂😂😂
Can't I say that a vector field F is conservative iff its Jacobian matrix is symetric? (equal to its transpose)
i want a picture of drawings on his shirt ,, but couldn't find online, guess couldn't search for right keywords
if anyone knows please share the link
if the curl of the function gives (...)i = (...) j = (...)k , then the forces are conservative.
where did you get the shirt, i need itttttttt
INSAHLLAH I PASS CALC 3 FINAL BABY LETS GOOOOOOOOOOOOOOOOOOOOOOOOOOOO
If the last equation is eP/ex = eM/ez instead of eM/ez = eP/ex, then the whole equations look like a cyclic fashion and would be easy to be memorized.
I love your t shirt
the thing which is like most is his 't-shirt'
That is such a cool shirt haha
Now I get it. Electric field is a flux field and Magnetic field is a flow field. Can't wait to see the nature of potential function of both 🤯
How do we test to see if a field is conservative ? The answer is to check, if the curl of that vector field gives us a zero vector !
Indeed, that is exactly the same as what I've done here, and we'll inroduce the curl a little later in the playlist.
please link your tshirt
your shirt is so cute
Excellent! And I love your clothes!
This kind of math speak is exactly why I hate pure math. Nobody ever explains concepts in words anymore. It's all these weird symbols and logic statements that humans aren't meant to understand. At least engineering has intuitive diagrams and they actually tell you what youre looking for.
Anyways, I'm so glad that this is going to be my last semester of dealing with this BS. Thanks for the video, it helped.
Head hurty.
this was such a waste of time
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Thank you