Ciro Santilli @cirosantilli  40

This is how you transform the Lagrangian into the Hamiltonian.

Subtle is the Lord by Abraham Pais (1982) chapter 4 "Entropy and Probability" mentions well how Boltzmann first thought that the second law was an actual base physical law of the universe while he was calculating numerical stuff for it, including as late as 1872.

But then he saw an argument by Johann Joseph Loschmidt that given the time reversibility of classical mechanics, and because they were thinking of atoms as classical balls as in the kinetic theory of gases, then there always exist a valid physical state where entropy decreases, by just reversing the direction of time and all particle speeds.

So from this he understood that the second law can only be probabilistic, and not a fundamental law of physics, which he published clearly in 1877.

Musk is a truly ambivalent personality. Some points are very good. Some are very bad.

Respect on the technical side by Ciro Santilli.

But the way he treated his first wife Justine Musk, is very very weird, incomprehensible: www.marieclaire.com/sex-love/a5380/millionaire-starter-wife/

Positive Cirocoins for possibly going to reverse Twitter's unfair Trump ban if his Twitter acquisition goes through:

Negative Cirocoins for according to Wikipedia:

www.urbandictionary.com/define.php?term=turd%20polishing on Urban Dictionary.

Ciro Santilli learned this expression from Angry Video Game Nerd.

First we write a vector field as:Note how we are denoting each component of $F$ as $F^i$ with a raised index.

Then, the divergence can be written in Einstein notation as:

It is common to just omit the variables of the function, so we tend to just say:or equivalently when referring just to the operator:

Consider a real valued function of three variables:

Its Laplacian can be written as:

It is common to just omit the variables of the function, so we tend to just say:or equivalently when referring just to the operator:

Set of eigenvalues of a linear operator.

The general result from eigendecomposition of a matrix:becomes:where $O$ is an orthogonal matrix, and therefore has $O^{-1}=O^T$.