Derivation of the divergence and curl of a vector field in polar coordinates. Join me on Coursera: imp.i384100.ne... Lecture notes at www.math.ust.hk... Paperback at www.amazon.com... Subscribe to my channel: www.youtube.com...
I was in my first year of a physics degree 20 years ago. I wasn’t that motivated in the field and I changed direction to medicine. Revisiting these topics now is satisfying . These videos are excellent.
Regarding Equation of Divergence, Shall it 2 terms as per Dot product definition ∇.U= (r^ ∂/∂r + θ^ ∂/∂r 1/r) . ( Ur r^ + Uθ ∂/∂θ) = r^ ∂Ur/∂r + θ^ ∂U θ /∂r 1/r Why we make complete multiplications for two parts of divergence?
As per the dot product definition earlier explained, the cartesian coordinates were independent of each other. In polar coordinates, however r is dependent on theta. Hence you need to derive theta and r terms by theta and r, giving you four terms as per my understanding.
Dear Professor Chasnov, what a great resource, thank you very much. My Question: At 4:55 in the video you state the unit vectors are independent of "r" and you disregard the d/dr contribution. (presumably because the d/dr of a constant = 0). It is not obvious to me why the unit vectors are independent of "r". Can you please point me to a resource that might explain this further? Much Thanks! Kind regards, Rick
