Hilbert Book Model Project/Slide F2

Hilbert Book Model Project

F2

The terms of the first oder partial differential equation get names and symbols
${\color {white}{\vec {\nabla }}\psi _{r}}$ is the gradient of ${\color {white}\psi _{r}}$	${\color {white}\langle {\vec {\nabla }},{\vec {\psi }}\rangle }$ is the divergence of ${\color {white}{\vec {\psi }}}$
${\color {white}{\vec {B}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\vec {\nabla }}\times {\vec {\psi }}}$ is the curl of ${\color {white}{\vec {\psi }}}$	${\color {white}{\vec {E}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ -\nabla _{r}{\vec {\psi }}-{\vec {\nabla }}\psi _{r}}$
Faraday ${\color {white}{\vec {J}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\vec {\nabla }}\times {\vec {B}}-\nabla _{r}{\vec {E}}}$	${\color {white}{\vec {\nabla }}\times {\vec {E}}=-\nabla _{r}{\vec {B}}}$
${\color {white}{\vec {\nabla }}\times {\vec {E}}=-\nabla _{r}{\vec {B}}}$	${\color {white}\nabla _{r}{\vec {B}}={\vec {\nabla }}\times (\nabla _{r}{\vec {\psi }})=-{\vec {\nabla }}\times {\vec {E}}}$
${\color {white}{\vec {F}}=q\,{\vec {E}}+q\,{\vec {v}}\times {\vec {B}}}$ is the Lorentz force
These equations look like Maxwell-like equations but in fact, they are quaternionic partial differential equations