Inexact Differentials

Any function f has a differential, df. But we can also write down differential quantities, which we label đf or δf, that are not actually the differential of any function f. These are called inexact differentials.

[@colorx6030]

Just recently learned about Exact Differentials and the first part of this video was an interesting perspective. It made sense. Also, I now realize why there aren't as many videos about Inexact differentials: if a differential isn't exact, you don't really solve it any further. You just state that it is inexact then just move on. Thanks!

[@PhysicalChemistry]

Yes, it's often not productive to do math with inexact differentials. To paraphrase Tolstoy: all exact differentials are alike (and obey calculus rules). Each inexact differential is inexact in its own way.

[@piratesofphysics4100]

the moment you made me realize that maybe I can't go back to the same function all the time I instantly hit the like button and subscribed

[@PhysicalChemistry]

Thanks, I'm glad you got something out of it

[@hemadhumal4036]

Same 😅

[@superpanda9810]

You explained the concept very coherently thank you

[@PhysicalChemistry]

Great, glad to hear it

[@wunks7]

Found this to be useful. Thanks.

[@PhysicalChemistry]

Good to hear

[@shauryachaturvedi6048]

been searching for something like , the explanation everyone gets

[@PhysicalChemistry]

Glad to hear it clicks for you

[@odecody517]

thank you for an excellent lecture

[@PhysicalChemistry]

You're quite welcome

[@mranonymous_25]

Thanks for such a great explanation

[@PhysicalChemistry]

Glad it was helpful!

[@EzraMahina]

❤

[@sofiv95]

This was very easy to understand for me, thank you

[@PP-op1ql]

Hi. What is the sign after 1st part of 3rd function? I am asking because I can't see it. I would be grateful if someone could tell me :).

[@PhysicalChemistry]

Do you mean @4:46, the function in pink in the upper right? That's not a sign, it's the word "or". The idea is that f(x,y) must be 3xy² if you integrate the dx term, but it must be 6xy² if you integrate the dy term. It can't be both at the same time, which is why df is an inexact differential.

[@sourish_mitra]

Thank you very much, Sir

[@PhysicalChemistry]

You are most welcome

[@urcringebro4706]

thank you

[@PhysicalChemistry]

you're welcome