totally what I was looking for, to study how did volume element dv, came out at (r^2)(dr)(sin theta)(d theta)(d phi), as expressed while evaluating the radial probability distribution function, in quantum mechanics. You are a life Saver!
Thank you for the video. I have a question. If you take a large (equilateral) tetrahedron and displace the volume of a sphere so that the point of the tetrahedron converges with the center of the sphere, what percentage of the sphere's total volume will be displaced by volume of the tetrahedron?🤔
May Allah's peace, mercy and blessings be upon you, thank you very much. I just want to know the proof that multiplying the equation by the "sin (θ) " is the correct one because many of the functions have the same property (f (0) = 0, f (pi / 2) =1) . I somehow came to prove this(that was in 2013, when I was in the university), but I don’t know if my knowledge of it in advance had an effect. (I want to know the correct way to prove it), maybe there are many others who want that and can't find where, I think you are the most suitable one. Thanks again.
Thank you. Sometimes it is sufficient to use the properties of the function and test it at the end points. You need a function that goes to zero when the angle is zero (parallel to the z-axis). And you need a function that goes to 1 when then angle is 90 degrees, (along the x-y plane). The sin function will do that and thus it is the correct function.
If I could, I would give you a million likes. Thanks for doing these videos, they are life savers.
We appreciate your one like 🙂
The thumbnail is so clear that you can understand the whole thing from there
Thank my wife. She makes all the thumbnails.
@@MichelvanBiezen just let her know, she is awesome. Great tutorial btw✨
Thanks a lot! Couldn't find it anywhere online and came across this video after about an hour of searching. You explained everything so clearly :)
Glad you found our videos! Pass the word! 🙂
I just want to appreciate you, thanks for making these videos.
Our pleasure!
thank you for explaining sin theta. nowhere else, videos or textbooks, explains this extra number.
Glad it was helpful! 🙂
totally what I was looking for, to study how did volume element dv, came out at (r^2)(dr)(sin theta)(d theta)(d phi), as expressed while evaluating the radial probability distribution function, in quantum mechanics. You are a life Saver!
Thanks!
Thanks for making all of these available. I am grateful for these lectures.
You're most welcome!
thank you I could not find where the sin comes from anywhere. greatly appreciated
Glad we could help
I appreciate all your efforts.
Thank you and welcome.
Thank you so much for your videos!! ahh I can't describe how helpful your videos are!
Very well and clearly explained, thanks!
Glad you enjoyed it!
Explained it very well.. Thanks ❤️
My pleasure 😊
This video save my time very much. Is there any way to prove this mathematically?
thanks for this, sraight to the point and intuitive!
Glad it was helpful!
Is the quadrangle bound by 4 great circles? I want to know if d-theta is bound by latitude or great circles.
thanku sm, really good explanation
You're most welcome
Thank you Sir
Very well explained
You are welcome. Glad you liked it.
Thanks sir for your nice videos you are a legend sir
Keep it up sir👍👍
Thanks and welcome
Thank you for the video. I have a question. If you take a large (equilateral) tetrahedron and displace the volume of a sphere so that the point of the tetrahedron converges with the center of the sphere, what percentage of the sphere's total volume will be displaced by volume of the tetrahedron?🤔
Thank you professor
You are very welcome
Thank you Sir😊
Most welcome
Can you please tell problems on divergence theorem in cylindrical coordinates
Specific applications of these theories will come in future chapters, when we have time to develop them.
MUCHAS GRACIAS!!!
You are welcome. Glad you found our videos.
May Allah's peace, mercy and blessings be upon you, thank you very much. I just want to know the proof that multiplying the equation by the "sin (θ) " is the correct one because many of the functions have the same property (f (0) = 0, f (pi / 2) =1) . I somehow came to prove this(that was in 2013, when I was in the university), but I don’t know if my knowledge of it in advance had an effect. (I want to know the correct way to prove it), maybe there are many others who want that and can't find where, I think you are the most suitable one. Thanks again.
Thank you. Sometimes it is sufficient to use the properties of the function and test it at the end points. You need a function that goes to zero when the angle is zero (parallel to the z-axis). And you need a function that goes to 1 when then angle is 90 degrees, (along the x-y plane). The sin function will do that and thus it is the correct function.
May I ask why is the area element in spherical coordinates the same as the volume element in spherical coordinates
They cannot be the same because the units must be m^2 for area and m^3 for volume.
Hello! Why when we take double integral to come up with formula A = 4*pi*R^2 our r is constant
If we are calculating the surface area and the shape is a sphere, r will be constant.
@@MichelvanBiezen i can not understand why r is constant. for example when we do triple integrall r is not constant
Every point on the surface of the sphere is equal distant from the center of the sphere. (That is why r is constant).
Masterclass
Sir, dA=d(theta)*d(phi), right?
What is the need of taking 'r' ?
No, dA = r d(theta) d(phi) sin(theta)
@@MichelvanBiezen But,how?
For arc length you need the equation: s = R x theta
thank you
You're welcome
❤❤❤❤
Thank you. 🙂
i still have no idea whats going on TTTTTT
Thank you Sir ❤️
Most welcome 🙂