The Laplace Operator, Divergence, and Curl

In this video we discuss 3 important vector derivative operations, the Laplace operator, the divergence of a vector field, and the curl of a vector field.

Topics and timestamps:
0:00 – The Laplace operator
8:51 – Divergence of a vector field
18:18 – Curl of a vector field

#Calculus

[jacobgivens]

AE 501, I forgot to send a comment on this video when I originally watched it, so I making one now. But this really helped with the homework, thank you!

[Andrew_Bruns]

AE501: Great refresher and discussion on the notations for the laplace operator and divergence

[EfremNickel]

AE501: It was nice to come back to this lecture video after the Potential Functions video. Definitely helped connect the dots!

[KennethWright-kh]

AE501: Thanks for clarifying the notation. I always forget about the importance of the dot.

[Clipaholick]

Amazing! I love vector calculus and you're a great teacher.

[MagdaleneRachelleShelton]

AE501: The notes example for fluid on a wavy wall was interesting!! -Maggie Shelton

[LilanieAlfredaAbdur-Rahman]

AE501: That was a great review. Where did we intro potential functions? It and the curl concept were sources of confusion in aerodynamics so re-learning these fundamental concepts before more advance coursework is welcomed.

[kenankenan]

This is why engineering mathematics in universities should be teach by engineers or applied mathematicians. Sometimes some universities allowing pure mathematicians to teach math to engineers and we all know the results. Pure mathematics a bit boring for engineers .We need more intuition rather than rigor. Dear Cristopher your tutorials are brilliant. Ur approach is real engineering approach. Thanks god that we have such professors like u . God bless you dear professor

[GiovanniRiggi-jq]

AE: 501B - Johnny Riggi. never went through the way these operators are related to each other in undergrad. This video was a great intro on the subject!

[changlongwang]

[A E 501 student] Hi Professor Lum, at the time stamp 4:51, should the expression of the attractive force vector p bar have a overall negative sign, otherwise it looks like a repelling force. Well, the missing negative sign won't matter to the equation del^2 f = 0 because of the zero on its right hand side. Thank you! - CW

[abdul-haleemsabirbaloch]

I need lecture of curvilinear coordinate system😊

[TriMartz-fx]

[AE501] Is it correct to think of the divergence operator an extension of the dot product and the curl operator as an extension of the cross product? if so, within this framework, what is the gradient analogous to?

[shreyaskatiyar]

Professor! Can u get me the link of dc motor modelling using control theory if you have. I am unable to find it in playlists.