to anyone interested in the algebraic use of differentials i would suggest reading keislers elementary infinitesimal calculus which is free online. basically you can define differentials in terms of infinitesimals where an infinitesimal € has the property €
Nice video! I am a pretty mathematically rigorous person and it always annoys me when people (especially teachers) multiply by dx or dt without understanding what that step really means, I feel very reassured knowing that someone else is rigorous about this too and knows the difference
@@MarkusJaeger-itguy well, if u compare it via the schools and national curriculum textbooks (NCERT here) they dont even Fking mention it. Sal introduces to almost ALLL nukes and corners to the subject. So, cant say about u, but i am thankful to him for implementing this mindset in his teachings.
4:15 Starting from chain rule in derivatives, i never felt weird doing that. is it okay?? 'Cz chain rule there, is just dividing and multiplying by dt. Ever thought like that 😅?? as it was discouraged to do that with dimensions too (treating algebraically), and later it was taught that "Do this with dimensions too" (dimensional Analysis).
So, now my mindset has become that i will do what seems right, cause they take turns about what they say wrong later as it was not wrong, they were just not informing about it as it was advanced.
this is definitely more helpful than any calc teacher has been.. should've taught us this from the outset
to anyone interested in the algebraic use of differentials i would suggest reading keislers elementary infinitesimal calculus which is free online. basically you can define differentials in terms of infinitesimals where an infinitesimal € has the property €
that book has almost 1000 pages!!
Omg i have been looking for this for 2 days, and it took right keywords to type so that it showed up.
Could you please explain why can't we treat differentials as algebraic expressions and when it is right to do that
It would be great 🙏🙏
take a shot every time he says "rigor"
I did,and blacked out 🤔
The reason why I can't accept this expression is a fact that "dy = f'(y) dx" is circular resoning. But it works well for the Physics.
Where can I get some rigor?
My question same, and its been two years, did you found out????
"Too complicated to explain" and doesn't give any 'further reading' options. Pisses me off quite a bit.
Nice video! I am a pretty mathematically rigorous person and it always annoys me when people (especially teachers) multiply by dx or dt without understanding what that step really means, I feel very reassured knowing that someone else is rigorous about this too and knows the difference
well... he did not really explain, just said that the explanation would be too complicated and handwavy. At least he mentioned it.
@@MarkusJaeger-itguy exactly my friend, and i am almost crying😭😭😭😭
@@MarkusJaeger-itguy well, if u compare it via the schools and national curriculum textbooks (NCERT here) they dont even Fking mention it. Sal introduces to almost ALLL nukes and corners to the subject. So, cant say about u, but i am thankful to him for implementing this mindset in his teachings.
This makes sense
What about the case when we take the second derivative? Are the differentials still treated algebraically and how?
what app is he using it seems helpful I want to get it
So what would ∫dx be if you did integrate both sides of ∫1/y dy = ∫ dx ?
it would just be x+C
4:15 Starting from chain rule in derivatives, i never felt weird doing that. is it okay?? 'Cz chain rule there, is just dividing and multiplying by dt. Ever thought like that 😅??
as it was discouraged to do that with dimensions too (treating algebraically), and later it was taught that "Do this with dimensions too" (dimensional Analysis).
So, now my mindset has become that i will do what seems right, cause they take turns about what they say wrong later as it was not wrong, they were just not informing about it as it was advanced.
does dy/dx = z mean that dx/dy = 1/z?
George Steele yes as long as z doesn't equal zero
first like
No.