Newton's notation

Newton's notation for differentiation, or dot notation, uses a dot placed over a function name to denote the time derivative of that function. Newton referred to this as a fluxion.

Isaac Newton's notation is mainly used in mechanics. It is defined as:

$\dot{x} = \frac{dx}{dt} = x'(t)$

$\ddot{x} = \frac{d^2x}{dt^2} = x''(t)\,$

and so on.

Dot notation is not very useful for higher-order derivatives, but in mechanics and other engineering fields, the use of higher than second-order derivatives is limited.

Newton did not develop a standard mathematical notation for integration but used many different notations; however, the widely adopted notation is Leibniz's notation for integration.

In physics, macroeconomics and other fields, Newton's notation is used mostly for time derivatives, as opposed to slope or position derivatives.

Newton's notation

See also