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In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence written in the form = = () = = ()! where is the ...
If the fluent is defined as = (where is time) the fluxion (derivative) at = is: ˙ = = (+) (+) = + + + = + Here is an infinitely small amount of time. [6] So, the term is second order infinite small term and according to Newton, we can now ignore because of its second order infinite smallness comparing to first order infinite smallness of . [7]
For a period of time encompassing Newton's working life, the discipline of analysis was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Newton's introduction of the notions "fluent" and "fluxion" in his 1736 book. A fluent is a time-varying quantity or variable. [1] The term was used by Isaac Newton in his early calculus to describe his form of a function. [2]
Newtonian mechanics; universal gravitation; calculus; Newton's laws of motion; optics; binomial series; Principia; Newton's method; Newton's law of cooling; Newton's identities; Newton's metal; Newton line; Newton–Gauss line; Newtonian fluid; Newton's rings; Standing on the shoulders of giants; List of all other works and concepts
Newton's series may refer to: The Newton series for finite differences, used in interpolation theory. The binomial series, first proved by Isaac Newton.
Newtonian cosmology; Newtonian dynamics; Newtonian fluid, a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear Non-Newtonian fluids, in which the viscosity changes with the applied shear force; Newtonian mechanics, also known as classical mechanics