Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl] 

Underrated comment 😂

That's interesting.... someone with only a high school formal education could extended or expanded on Maxwell's equation. I think it's a bit easier, if you're born in the late 1800s to the early 1900s. From the 1800s to the early/mid 1900-ish, I think really smart individuals were able to learn, large on their own (or with only high school or undergraduate levels of formal education), deep mathematics. Ramanujan was one & the late Freeman Dyson was the other, both rare talents. I believe it was said, even while Dyson was alive a couple years back, that he was the "last professional mathematician" to never have formally earned a PhD in mathematics. I think part of the story was that he was too eccentric, to want to spend years under someone who's going to tell him to think or do things he didn't want to; it could also be that his formal studies (for an advanced degree, for example), was "interrupted" in the late 1930s to mid 40s, when he started working with giants like Feynman, Hans Bethe, Fermi, Teller, Lawrence, Fucs, Seaborg, Oppenheimer et al in the Manhattan Project & related Pentagon works.... I believe it was Freeman Dyson who recounted, later on in life, that among that exceptional group, the soft spoken, ever-courteous Hans Bethe --- with a thick German accent --- was the one with seemingly photographic memory who didn't need to refer to tables or notes or books on the various numbers (atomic weight, melting point, boiling point, density, electronegativity, ionization, thermal conductivity, etc.) of the various major elements they're working on.... because he had all those numbers in his head!

Think of all original mathematicians who formulated the knowledge we know today. What schools did they attend and what teachers did they have to help them come up with their fantastic exploration and knowledge? Schools are great when they serve as a motivator to learn and a supplement to hard work and creativity. When there is no interest, no hard work or no creativity, schools are just another wasteful spending. Deeper understanding of any subject requires curiosity, further reading and much contemplation. I kept my textbooks and visit them once every while to reformulate what I have learned and put it in a different perspective. I love it when I see things the second round differently and more broadly or abstractly. Mathematics specifically is a subject that is full of amusement and applicability. The same subject could be generalized and applied in so many novel ways as deeper understanding achieved.

After I have completed my msc in Chemistry and more then after that silly thing I got something intuitive approach to calculus, imagination with calculus is Great 👍

It's not that simple... at least for Heaviside's contribution to vector calculus. Yes, he became to strongly go against quaternions (which IMO are easier to understand, if you already know vector calc.) ... but, Heaviside wasn't the only one trying to explicate Maxwell's equations, by using vector calculus. Heaviside was... for a time... forgotten... and he made many important contributions to eletro-magnetics... but the history of his work is sometimes popularized incorrectly.

The best explanation from someone who’s already seen it before kind of comment lol

Glad you liked it!

Dr Brunton is also a great professor for teaching....

we need this in 12th grade in India for Jee Exam

You're welcome! Thanks for watching :)

Thanks for watching!

Thanks! And good catch on the reference -- that just goes to show your excellent and refined taste ;)

hummm thank you sir

"Lll-literally" looking forward lol 😜 jk, my sentiments echoed. Love these videos

This is so cool thank you again sir! Looking forward to more videos on this.. I was doing data foundations and I wish I had started with this intuitive understanding of vector calculus

Thank you for your kind words :)

Thanks!

@@Eigensteve so to get slightly more specific, I'd say that I don't recall one prof who made any effort to explain the application of the tool. Just, this is the tool, this is how you do the mathy part, and this is the answer. I didn't make physical sense of any of this until many years after and had to do it on my own.

This is so cool -- I love learning new things from the comments. Thanks!

The nabla symbol is used with different meanings in a few other contexts, like theoretical computer science. Del specifically refers to the nabla symbol used in vector calculus.