23: Scalar and Vector Field Surface Integrals - Valuable Vector Calculus
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- Опубліковано 7 сер 2024
- Video on scalar field line integrals: • 20: Scalar Field Line ...
Vector field line integrals: • 21: Vector Field Line ...
Video on double integrals: • 16: Double Integrals -...
An explanation of how to calculate surface integrals in scalar and vector fields. We go over where the formulas come from and how to actually get to an answer!
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Timestamps:
0:00 Scalar fields
14:18 Vector fields
Music: C418 - Pr Department
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.
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.
Excellent. Clear and to the point. No frills needed.
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
Increíble!!! 💯
Muy bien explicado, súper recomendado.
I spent four years doing a physics degree starting in 2003. UA-cam 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 .
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!
Amazingly and beautifully explained. Thanks professor.
Wow!! You explained this so nicely man!!!
brilliant! I think I'm going to watch all of your videos just for fun.
U rock brother! Thanks a lot for making such videos. It inspires me a lot. Thank u vei much.!
Great Lecture Sir. Respect
this video saved me before my final. Its so much easier than I thought! Amazing explanation thank you
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
Fair explanation.
holy shit, how can someone explain something so good and so fast, propss my man!!
thanks for this explanation video!
great video.. many things got cleared here.
Thanks a lot！You are the best！
Excellent Video, Thanks a lot🎉
Thank you for this videos,beacuse of you i am planning to study mathematics
thanks for such clear explanation.
Thank u sir ...your lecture is very helpfull ,....Everything is clear now ....
Just like line integrals can be thought of as a chain of varying density, a surface integral can be a curved sheet with varying density.
but I like the idea of flattening the surface onto 2-D and getting its height as a function of 2-D location
best explanation for surface integrals
Beautiful 🎉
Thank you from Algeria , this is really helping me 💗
Beyond excellent😍😍
Great vid
Very nice
Thank you
Awesome
This explanation is unique all you tube video
Love u sir.
Given 2 likes from two id...
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?
Great
so what does the surface integral on scalar field and surface integral on vector field gives us ??
What is the difference between left hand side and right hand side
I like this
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!
See Fubini's Theorem
Thanks for the video. However, I found that the first surface integral is equal to 48π for some reason. What did I do wrong?
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?
Yes; we can think of taking the parallelogram in terms of u,v and evaluating r(u,v) for each corner.
Riemann hypothesis, please.
At 7:00 , shouldn't the parallelogram's endpoints be r(u, v), r(u+du, v) etc?
That's correct. As is implied at 4:09, I'm using the ordered pairs as shorthand for the corresponding points on the surface.
thank you very much, ARE you s university professor? which university?
You are wow...!
This is also called shadow integral can you please explain that too
Does the magnitude of cross product in the surface integral have anything to do with the Jacobian..It seems to be similar ones
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!
@@MuPrimeMath
Thats Cool😍💕
I have one problem.. can you solve it for me please?!
❤️
So the reason I was having trouble visualizing a surface integral is because I'm not a 4-dimensional being. That makes sense.
...as y²
is || ru x rv || = || rv x ru ||
thank you
The cross product is anticommutative, meaning that b × a = -(a × b). As a result, the magnitudes of the two are equal.
yeo caltech class of 2024!!
tsaL
Oops I found it; I forgot to square the 4 in (4sin(theta))²
The result of the last example is 12π not 9π.
Both of the integrals shown at 26:38 evaluate to 9pi
@@MuPrimeMath OK, I see my error: the z in the first component of the vector field looks like a 2 so instead of z/x, I wrote 2/x.
Pretty sure not four dimensions… still two dimensions even though in 3D
i going to faillllll!
Sorry, but I'm disappointed in your explanation of a surface integral over a vector field ... I've seen better ...