# Hilbert Book Model Project/Slide F2

hbmp
Hilbert Book Model Project
F2

The terms of the first oder partial differential equation
get names and symbols

${\displaystyle {\color {white}{\vec {\nabla }}\psi _{r}}}$ is the gradient of ${\displaystyle {\color {white}\psi _{r}}}$

${\displaystyle {\color {white}\langle {\vec {\nabla }},{\vec {\psi }}\rangle }}$ is the divergence of ${\displaystyle {\color {white}{\vec {\psi }}}}$

${\displaystyle {\color {white}{\vec {B}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\vec {\nabla }}\times {\vec {\psi }}}}$ is the curl of ${\displaystyle {\color {white}{\vec {\psi }}}}$

${\displaystyle {\color {white}{\vec {E}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ -\nabla _{r}{\vec {\psi }}-{\vec {\nabla }}\psi _{r}}}$

Faraday ${\displaystyle {\color {white}{\vec {J}}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\vec {\nabla }}\times {\vec {B}}-\nabla _{r}{\vec {E}}}}$

${\displaystyle {\color {white}{\vec {\nabla }}\times {\vec {E}}=-\nabla _{r}{\vec {B}}}}$

${\displaystyle {\color {white}{\vec {\nabla }}\times {\vec {E}}=-\nabla _{r}{\vec {B}}}}$

${\displaystyle {\color {white}\nabla _{r}{\vec {B}}={\vec {\nabla }}\times (\nabla _{r}{\vec {\psi }})=-{\vec {\nabla }}\times {\vec {E}}}}$

${\displaystyle {\color {white}{\vec {F}}=q\,{\vec {E}}+q\,{\vec {v}}\times {\vec {B}}}}$ is the Lorentz force

These equations look like Maxwell-like equations but in fact,
they are quaternionic partial differential equations

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