Explanation of divergence in cylindrical coordinates - where does the formula come from?

[@olenabv6825]

Excellent film, a small typo at the end in final formula (missing 1/rho) in 2nd term.

[@craignurehall8934]

This is really helpful, but why is it obvious to insert 1/r with the theta partial derivative in the initial operator?

[@paolofernandofloresrivera6244]

por que el arco se define como R(theta) entonces la el diferencial del arco es rdiferencial de theta

[@Remains123]

@@paolofernandofloresrivera6244 Yo no entiendo por qué "multiplica" el primer término de nabla por cada uno de los términos del otro vector, no se supone que el producto punto es coordenada a coordenada ?

[@Janfissette]

thanks, helped me a lot! (needed this in fluid dynamics)

[@tanmaybhise]

Thanks a lot for the explanation. Was looking for this explanation for a long time

[@DaHornsOfdVan]

Oh man, this helped me a LOT for understanding curvilinear continuum mechanics! Thank you so much!

[@jkjsooner]

I have always wondered why the rho is within the derivative. The shorthand is very misleading. Thank you so much for pointing this out.

[@ee4life623]

I like the video a lot, thumbs up, but why is it obvious the 1/rho in the operator for cylindrical coordinates? Is there some proof or reason for why its there?

[@danielsteinfeld1445]

Thanks!! Needed it for atmospheric dynamics

[@Nickesponja]

You saved my life, thank you!!!

[@evencloutier4145]

I don't understand why the dot product of the Del operator with the field vector gives 9 terms... shouldn't it be only three (Del term in direction of Rho with the component Rho of the vector, Theta with Theta and z with z)?
That is : (dr, dt, dz).(Ar, At, Az)= dr.Ar + dp.At + dz.Az
This is how the dot product usually work, is there a special rule for the Del operator?
why do we end up with: dr.Ar + dr.At +dr.Az + dt.Ar + dt.At + dt.Az + dz.At + dz.At + dz.Az ?

[@ananthsm2007]

Great video, thanks :) But there is a 1/r missing in second term of last eqn.

[@sarang5693]

Thanks sir...really well explained

[@jamesjoetomo]

Thx, this tutorial reaaaallyy helped me

[@bomgulder]

Thank you. It helps me out

[@eun1908]

What a nice video!!!

[@prof.irineujunior794]

Thank you. Very helpful.

[@MrMattBiemans]

Thanks! This was very useful

[@alexandrospapadopoulos5060]

Thank you !!!I did the same mistake too ..

[@akashkadambi3732]

Thanks u very muchhhhhhhh....h tends to infinity 🙏🙏🙏🙏🙏🙏

[@AliceWonderland1899]

thanks a lot! really helped me!

[@laliash9361]

a lot of thanks to u
yr work go great

[@홍우진-v3h]

i think the last equation is wrong. There is a missing part 1/r at theta part

[@medkha8210]

that's because he forgot the 1/r in the second line (theta line ), however when he correct it , he only work with it in the rho part, and forgot the theta part, so it isn't wrong i guess, he just didn't write it correctly :D

[@123dikshant]

Too long and boring

[@hkopenh08519]

myth explained!! thankss

[@mortezakhoshbin]

greaaaaaaaattttttt that was awesome

[@sdadas4986]

Russian math, best math

[@karancharlee]

wow

[@小江-j1i]

If you say they are all unit vectors, then it is nothing interesting.