Contour integration, Ramanujan Master theorem (Mellin transform), Hankel transform, fubini theorem for integrals and series, Maz identity (laplace transform), symetry (like king’s rule), integrating with floor and mantis, taking imaginary and real part for trigs, using riemann zeta, dirichlet eta and beta, euler gamma and beta, digamma, lerch zeta transcentential (hurwitz zeta and polylogs), generalized hypergeometric identyties (like clausen formula), Ti(x) , Ei(x) , Li(x), incomplete gamma functions, sometimes even fourier series expansion, mittag leffler expansion, weierstrass factoryzation, laurent series, jacobi triple product identity and so on… 😅
I wanna add a suggestion. In chapter two for the power rule derivation, I suggest using x^n for generalizing instead of finite trials. The idea is to use a binomial expansion for (x+h)^n while just blanking the infinite amount of middle terms (just write the first, second, and end terms). This will be x^n + nx^(n-1)h + nC2 x^(n-2) h^2 + ... + h^n. Later on, x^n will cancel and all the numerator expression will be divided by h. This will be nx^(n-1) + nC2 x^(n-2) h + ... + h^(n-1). When the limit h -> 0 is applied, the third to last terms disappear (which is why I said to just ignore the infinite number of middle terms) and the result will be nx^(n-1). This is to prove that the pattern works for all n ∈ R and not just some specific and coincidental values of n.
"now remember dx/dy is just a fraction" ahhhhh there it is, i see so you're a physicist/engineer after all. i know math majors in the replies starting a riot right now, don't worry bro i got your back fuck those elitist snobs, "it's not a fraction" BOOHOOO
I think it would be productive to talk about discrete differentiation (forward difference of a sequence) before talking about continuous differentiation.
@@jong7100 that's probably a third the reason why they tend to be fearsome and arcane if you ask me. continuous fundamental theorem of calculus takes a lecture to explain, discrete one is explainable in 5 minutes and is directly analogous
![[Live] : ONE 169 วันนี้!! "อนาโตลี vs อูมาร์"](http://i.ytimg.com/vi/IK3YZVWuFJg/mqdefault.jpg)
No matter how difficult differentiation gets, integration is always worse (u-sustitution, integration by parts, partial fractions, trig substitution, improper integrals, etc.).
Differentiation under the integral sign, laplace transforms, weierstraus subtitution....
Contour integration, Ramanujan Master theorem (Mellin transform), Hankel transform, fubini theorem for integrals and series, Maz identity (laplace transform), symetry (like king’s rule), integrating with floor and mantis, taking imaginary and real part for trigs, using riemann zeta, dirichlet eta and beta, euler gamma and beta, digamma, lerch zeta transcentential (hurwitz zeta and polylogs), generalized hypergeometric identyties (like clausen formula), Ti(x) , Ei(x) , Li(x), incomplete gamma functions, sometimes even fourier series expansion, mittag leffler expansion, weierstrass factoryzation, laurent series, jacobi triple product identity and so on… 😅
I wanna add a suggestion. In chapter two for the power rule derivation, I suggest using x^n for generalizing instead of finite trials. The idea is to use a binomial expansion for (x+h)^n while just blanking the infinite amount of middle terms (just write the first, second, and end terms). This will be x^n + nx^(n-1)h + nC2 x^(n-2) h^2 + ... + h^n. Later on, x^n will cancel and all the numerator expression will be divided by h. This will be nx^(n-1) + nC2 x^(n-2) h + ... + h^(n-1). When the limit h -> 0 is applied, the third to last terms disappear (which is why I said to just ignore the infinite number of middle terms) and the result will be nx^(n-1). This is to prove that the pattern works for all n ∈ R and not just some specific and coincidental values of n.
This is a very valid proof indeed!
bro you really makes me feel maths!!!
this was super helpful, thanks
dy/dx if y is a function of x: 😊
dω/dt if ω is a function of x, y, and z and the independent variables are defined parametrically as functions of t: 💀
Wonderful explanation and intuition behind the concept sir👍 wish your videos reach to more target audience
Thanks! It all takes time.
Excellent 😊
Did you ever read Sylvanus P Thompson?
No I haven't, what is it?
"now remember dx/dy is just a fraction" ahhhhh there it is, i see so you're a physicist/engineer after all. i know math majors in the replies starting a riot right now, don't worry bro i got your back fuck those elitist snobs, "it's not a fraction" BOOHOOO
I think it would be productive to talk about discrete differentiation (forward difference of a sequence) before talking about continuous differentiation.
Why's that? Calculus courses tend to teach continuous differential much earlier than finite differences such as Euler's method.
@@jong7100 that's probably a third the reason why they tend to be fearsome and arcane if you ask me. continuous fundamental theorem of calculus takes a lecture to explain, discrete one is explainable in 5 minutes and is directly analogous
Ok now do one for integration as well please.........
Short video but it's out now.
It's very basic but I like your explanation. Make videos which gives intuition about higher order derivatives and partial differential equations
Will do, thanks.
@@tuitia okay
Bro how do u make such videos? Like i am taking how u make equation transition?
Judging by the font he is using desmos
Great question. it's a combination of Manim, Desmos and Premiere Pro.
Naw man, you can't use the derivative as a fraction >:((((
There are a lot of things wrong with this.