Adv Diff Calc 7: Fundamental Lemma

Advanced Differential Calculus - Fundamental Lemma
In discussing about the concept of the total differential, there should be certain hypotheses which, when satisfied by a function, tell us whether a function has a total differential or is differentiable at a point (x, y).

This 'fundamental lemma' is just that and it is based on the continuity of partial derivatives.

Take heed in following the mathematical argument carefully.

Gassianmath.com - using numbers to solve the greatest mysteries.

Category:

Science & Technology

Tags:

• differential
• calculus
• advanced
• partial
• derivatives
• limit
• multivariable
• differentiation
• fundamental
• lemma

[simplystimpy]

I love how fast you go because it makes me really pay attention and not zone out. (who could zone out when you're going a hundred miles an hour!) Keep up the good work!

[donylee]

Yup, lots of people say I teach rather fast. But I guess the main reason is like what you said - keeping the mind in the zone.

Good preview. So what course your taking this fall, Real Analysis or Advanced Calculus?

[DoubleDutchBust]

O?First time eye met RosalieKeys

Fundamental LemmaKalielDance

ShewaswearingwhitePantsRedTop

Fundamental LemmaKalielDance

O?First time eye met RosalieKeys

E.O.Febreze as u can see 0:10

Adv Diff Calc 7: Fundamental Lemma

Rdonylee 3:23

[Marioag0412]

I'm a senior in high school mid-way through Calc two and I am proud to say that I both caught a few snippets and understood the proof as a whole, and yet was blown away by the analysis and correlative methods of this video!

[keep6rocks]

Bravo good sir

[Alif7845]

There's a Calc 7?! I'm only going to take Calc 2 my senior year.

[toopham]

I youtube fundamental lemma of langlands program and this video show up

[gremlinextreme101]

@MrSupaninja911 I know you posted this a year ago, but what he presents here is a lemma not a corollary, it is a proof that his previous videos assertion of continuity relies on, the theorem thus being proved. The chain rule would be a corollary...

[HXY241]

I wonder if you note the delta x and delta y in a wrong way in the geometry explanation. I think they should exchange the positions. You really give a excited lecture.thank you.

[nnostalgy]

thanx realy very important

[Eylexithymia]

Watching this guys is amazing but it also makes me feel like I'm nothing and I should quit life...

[VerraStrngNUCF]

this video is very helpful thank you for all of your time and effort

[carlorivera88]

muy rapido hablas