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Differential Equation

${\displaystyle \frac{dP}{dt}=kP}$

Differences between ${\displaystyle dP}$ an ${\displaystyle \mathrm{\Delta }P}$: ${\displaystyle \mathrm{\Delta }P}$ indicates to a measurable change rate for example ${\displaystyle 0.1}$, ${\displaystyle 2}$. It just describe the change. ${\displaystyle dP}$ in contrast, is a definition from differential equation, indicates to a infinitesimal quantity of change.

${\displaystyle dy=dx\ast f^{\prime }(x)}$

Which depict a approximate linear change, but not the real change.

Matrix

Additivity

Multiplication

Inversal