Newton's notation for differentiation

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

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's notation is mainly used in mechanics

Mechanics

Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

. It is defined as:

and so on.

Dot notation is not very useful for higher-order derivatives, but in mechanics and other engineering

Engineering

Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

fields, the use of higher than second-order derivatives is limited.

Newton did not develop a standard mathematical notation

Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...

for integration

Integral

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

but used many different notations; however, the widely adopted notation is Leibniz's notation for integration.

In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, macroeconomics

Macroeconomics

Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...

and other fields, Newton's notation is used mostly for time derivative

Time derivative

A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t\,.-Notation:...

s, as opposed to slope

Slope

In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....

or position derivative

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

See also