Ciro Santilli @cirosantilli  40

The total derivative of a function assigns for every point of the domain a linear map with same domain, which is the best linear approximation to the function value around this point, i.e. the tangent plane.

E.g. in 1D:and in 2D:

Music notation engine. domain-specific language input. The LaTeX of music.

Looking for formats that:

Bibliography:

Dominating awesome list: https-github-com-nodiscc-awesome-linuxaudio

A large part of these projects are on SourceForge as of 2020, it is scary. They just die.

Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.

Being a complex holomorphic function is an extremely strong condition.

The existence of the first derivative implies the existence of all derivatives.

Another extremely strong consequence is the identity theorem.

"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.

visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.

The key question is: how can this continuation be unique since we are defining the function outside of its original domain?

The answer is: due to the identity theorem.

Ciro Santilli sometimes fantasizes of having worked there in their golden years...

Original headquarters and laboratories: 463 West Street in New York, Manhattan area. On Surely You're Joking, Mr. Feynman Feynman mentions that in 1941 they could see the construction of the George Washington Bridge, presumably from that building, when William Shockley brought him over to visit to get a job there. However, the actual

Later:

Some interesting videos: