Wonderful stuff. As a non physics type I have like many others stared blankly at Maxwell's field equations. Here u not only go through the maths, so elegantly, but u give a clear explanation of what curl and divergence are. many thanks once again.
Also, if you forget you can think of the operator as a vector, which is the expanded matrix you gave... ["del" x F = curl F] and ["del" (dot) F = div F] ... they can be thought of as analogous to a dot product and cross product of the operator and F.. This also means div curl = 0 is like a scalar multiple...
my class doesnt have attendance but does have some stupid worksheet every day worth total 15% of our grade so I just come to class at the very end and fill that out and come home.
Something I noticed when you wrote PQR down the left and XYZ across the right: it looks like a Row Reduced Echelon Form (RREF) matrix at 10:29. Does that mean anything? Is it significant in any way or is it just by coincidence ? I would be really amazed if you could apply linear algebra in this part. Makes me wonder if math can be this beautiful or just coincidental.
Wait so the partial/partial(x,y,z) in the determinate are not the partials of the actual function? Well damn here I was getting super angry getting problems wrong in my book. I thought that was just a part of a formula this whole time and the people who wrote the book were just too lazy to write out the actual partials.
![Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]](/img/n.gif)
You're the best study partner, by the way.. You got me through Calc 1 and 2, now you're pulling me through calc 3!!! You should be paid LOL!
Awww thanks! I'm honored to help!
Thank you so much. You have contributed so much with my progress in Engineering Mathematics. I'm very grateful.
Thanks for letting me know!
The math is good and all, but the voice, its heavenly
You alongside organic chemistry tutor are the best .God bless you
Calc 3 happened many moons ago. Thanks for the quick, clear refresher.
+Bill Nolastname You're welcome!
Wonderful stuff. As a non physics type I have like many others stared blankly at Maxwell's field equations. Here u not only go through the maths, so elegantly, but u give a clear explanation of what curl and divergence are. many thanks once again.
Thank you so much, I'm so glad you enjoyed it!
Glad I found this channel. This was a topic I struggled with, but much clearer now. Thanks a million!
You're welcome, I'm so glad it's making more sense now! :D
Also, if you forget you can think of the operator as a vector, which is the expanded matrix you gave... ["del" x F = curl F] and ["del" (dot) F = div F] ... they can be thought of as analogous to a dot product and cross product of the operator and F.. This also means div curl = 0 is like a scalar multiple...
I try to review complex math once a month to keep myself sharp; you always deliver!
Wow never thought it'd be this easy. thank you! :D
This is why I skip math class. Why sit for an hour and not understand when I can watch a 12 min video and be able to do all my homework?
my class doesnt have attendance but does have some stupid worksheet every day worth total 15% of our grade so I just come to class at the very end and fill that out and come home.
Very true in this phase of the game of life.
Thank you so much. Your clear and effective voice helped a lot!
+ceres You're so welcome! Glad I could help.
You are a real life saver, our lecture's accent is so bad that none of us understands him
I've been there! I'm glad this is helping to fill in some of the gaps!
Thank you so much for explaining the difference between the formulas!! 8:13
Something I noticed when you wrote PQR down the left and XYZ across the right: it looks like a Row Reduced Echelon Form (RREF) matrix at 10:29. Does that mean anything? Is it significant in any way or is it just by coincidence ? I would be really amazed if you could apply linear algebra in this part. Makes me wonder if math can be this beautiful or just coincidental.
straight up, wasnt getting it in class but within 12mins im good
I'm so glad this helped clarify! :D
Nice matrix explenation on 11:08!
I will save this link!
Well explained 👍
Thanks for the review!
ur a lifesaver
Thank you!
your language is very simple for un-English people
Nice example, glad you posted this during my calc 3 semester! xD
I hope it helped! Good luck with the rest of Calc 3!
Thank you so much, you're getting me through college.
You're putting in the work! But I'm glad I can help along the way.
very helpful ! btw your handwriting is so good
+Patrick Wang Thanks!
thank you ❤
So, would optimized conditions of curl in a region have any significance such as the region's only axes of rotation?
Thank you
Finally, i understand! Thank you! :)
Oh good! I'm so glad it made sense! :D
Amazing at Calc 3!
calculus was not easy for me but thanks to krista king for the great explanation
+usman khokhar You're welcome, I hope it made it easier for you!
thanks! u saved me! i have test tomorrow
+Sheel Prajapati Good luck on your test!
+CalculusExpert.com
Your voice is amazing, you sound like an angel.
Thank you!!!
Stephanie Herrera You're welcome!
Determine the curl of F which is (V x F) at the point (2, 0, 3) given that
F = ze2xy i + 2xz cosyj +(x + 2y)k
Can you pls help me how can i solve it?
thank you thank you thank you
You are awesome!!!
Same to you! :)
Divergence at 9:36
can you please tell me what software you use for creating online black board... thanks a lot
+krishna chaitanya I explain here: kristakingmath.com/my-videos hope that helps!
what is youre software name you are teaching with?
Sketchbook, by Autodesk. :)
You're a math god. Come teach at my university instead.
i love you
So no derivation of the formulae for curl and divergence?
+Geekminer CurlF = X --> Which allows you to set up a determinant
DivF = dot
Wait so the partial/partial(x,y,z) in the determinate are not the partials of the actual function? Well damn here I was getting super angry getting problems wrong in my book. I thought that was just a part of a formula this whole time and the people who wrote the book were just too lazy to write out the actual partials.
I love u.
Why don't you use the term "determinant"? Then ppl can remeber how easy it is to calculate and not be scared of the term in the future. 😎