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Polar Coordinates (Divergence and Curl) | Lecture 27 | Vector Calculus for Engineers 

Jeffrey Chasnov
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Derivation of the divergence and curl of a vector field in polar coordinates.
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29 окт 2024

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Комментарии : 16   
@Dairy_of_quotes02
@Dairy_of_quotes02 3 года назад
Very helpful video ..I am from Indian in rural area ... thanks you so much I over country education is very expensive .we don't afford .like this ..👍
@strippins
@strippins 4 месяца назад
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.
@francobustamante1315
@francobustamante1315 3 года назад
Amazing video... but how do you write right in this glass?
@chrisye3974
@chrisye3974 2 года назад
Fantastic derivation! Thank you!
@junhee904
@junhee904 3 года назад
Very helpful! Thanks for nice video
@88noureldin
@88noureldin Год назад
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?
@88noureldin
@88noureldin Год назад
Same question for curl Where is definition of cross product (determinal of metrix) ?
@joeljohn6008
@joeljohn6008 2 месяца назад
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.
@ericzhang4464
@ericzhang4464 3 года назад
Thank you so much! Professor!
@RickP330
@RickP330 3 года назад
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
@ProfJeffreyChasnov
@ProfJeffreyChasnov 3 года назад
Look at their definition.
@RickP330
@RickP330 3 года назад
@@ProfJeffreyChasnov because the length (magnitude) is unity?
@shwetadidel3540
@shwetadidel3540 7 месяцев назад
Look at the definition of r^ and theta^...both are independent of r but depend on theta. Watch previous video
@SphereofTime
@SphereofTime 4 месяца назад
1:00
@88noureldin
@88noureldin Год назад
During Divergence formula , 1st term i think we consider ∂r^/∂r = 0 - can anybody remind me why ?
@shwetadidel3540
@shwetadidel3540 7 месяцев назад
Because r^ is a function of theta only as mentioned in the previous video.
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