Multivariable Calculus | The Jacobian

[@liviumircea6905]

This is a gem...like other people said this is the best content about Jacobian I found...Nice balance between intuition and formalism.Thank you very much Michael Penn

[@azmath2059]

Finally! A proper and concise explanation of the Jacobian! Thanks Michael.

[@pendawarrior]

Best explanation of the jacobian I've seen, thank you so much

[@thenateman27]

Mistake at 14:46, it should be a positive 2w

[@Hobbit183]

Really nice explanation, thanks

[@guvencagil]

Excellent. Thanks.

[@Sidd-rb4ec]

At 3:44 i don't understand why did we take tangent vector for the approximation

[@danv8718]

Because the tangent line always gives you the best approximation to a curve at a given point, in fact, if you zoom close enough, both will be indistinguishable. Zooming close enough is exactly what we do when we take the limit as the variables tend to zero and therefore the area of the rectangle and the area of the curvilinear region will match. Bottom line is all curvilinear lines look like straight lines if you get close enough.

[@programstix3837]

thank you

[@antoniocosta1447]

The final result should be 2w × (u×exp(2v) - u×exp(v + w + vw) )

[@ANTOINETTE-nk1tm]

YOU DO SOME REALLY NICE VIDEOS. YOU DON'T GO THROUGH EACH AND EVERY STEP, AND IT'S HARD FOR ME TO KEEP UP WITH YOU SOMETIMES, BUT THAT'S MY PROBLEM BECAUSE I'M SLOW, ; AN OVERALL YOU DO A GOOD JOB A LOT BETTER THAN OTHERS I SEE ON THIS CHANNELS. ONE THING I LIKE ABOUT YOU YOUR DEFINITIONS ARE VERY PRECISE. YOU DON'T MAKE MISTAKES.

[@РоманЛева-й9з]

Спасибо, хоть кто-то внятно проводит доказательства

[@tsunningwah3471]

diu

[@ANTOINETTE-nk1tm]

WELL DOGGY. I'LL BE DANG JIGGIED. THIS WAS A VERY GOOD VIDEO. I'LL BE DANG- JIGGIED !!!