This is the only clear explanation, I found on yt. I dont know why some profs dont give the visual intuition behind this, while its actually so easy to understand.
Because they themselves don't know these geometrical meanings ig. Each time when I try to debate on these visual intuitions with my professor, either he would roast me 😁 or try to end the session instantly. btw this man is doing great job. I learn a lot from this channel.
I watched the first part of this and due to the thing at 4:15, it was a bit hard to understand, but I eventually pieced it all together, it is a really complex topic to explain, you did a much better job then if I were to explain it, even if I were to write it down for my future self when I forget. This is the best I’ve seen on yotuube, by a large margin and trust me, I searched far and wide, excellent work!
That was brilliant. So concise and clear. Many thanks for passing on your insight into this topic. I shall watch that again and take notes. Really great lesson.
This video is still relevant even today (2024). Thank you for making the video. It has made me appreciate the concept of surface integral of a vector field
Maybe i'm not the originally targeted part of audince, as i have studied maths, so this things are fairly easy to me, as i'm only refreshing my memory, so i cannot give this channel a proper assessment, not content-wise anyway. When it comes to math, i'm quickly pleased. Channels such as this one, offers me a fun revising of theoretical stuff, with some examples. You might be thinking, why don't i just pick up some math text book. I would, but i'm very lazy. What i can say is your explanations are simply amazing. It is by how you are explaining this things show, how well you understand it on deeper, more intuitive level. And at your age... 😯 👏 bravo, just bravo
this was so useful, ive just started going over my notes and to understand multivriable calc and this was one of the best videos for surface integrals, way better than my lecterur. Youre saving my grades lol
I spent four years doing a physics degree starting in 2003. RU-vid existed since 2005 and this sort of content was certainly not available until after I finished. I always found the unengaging lectures difficult to follow, printed lecture notes missing insight and text books impossibly heavy. I wonder how much more I could have got out of that education had content like this been around to enhance conceptual understanding .
As far as I know, the order of double integral is not interchangeable. Maybe I could be missing some part of the video but which variable should I be integrate firstly when solving surface integral? Thank you very much!
Thank you for your excellent explanation videos! 🙏 One issue is confusing me: 4:15 when you start explaining the parallelogram in terms of u and v, do you actually mean r(u,v), r(u+du,v) etc, given that this parallelogram is on the surface S?
Hi, may I know how to solve this, if we do not parameterize it, instead we use the formula dS=sqrt(1 + (dz/dx)^2 + (dz/dy)^2 )dA? What should we substitute in order to eliminate z?
Yes, they are related! One way to think about a two-variable substitution (x,y) → (u,v) is to think of the original (x,y) region as a flat surface. Then the substitution is a parametrization that looks like r(u,v) = [ x(u,v), y(u,v), 0 ] If you compute the cross product rᵤ x rᵥ, it ends up being equal to the Jacobian in two dimensions!
