Fluent (mathematics)

Differential

Definitions
Derivative (generalizations) Differential infinitesimal of a function total
Concepts
Differentiation notation Second derivative Third derivative Change of variables Implicit differentiation Related rates Taylor's theorem
Rules and identities
Sum Product Chain Power Quotient Inverse General Leibniz Faà di Bruno's formula

Integral

Definitions
Lists of integrals
Antiderivative Integral (improper) Riemann integral Lebesgue integration Contour integration
Integration by
Parts Discs Cylindrical shells Substitution (trigonometric) Partial fractions Order Reduction formulae

Series

Convergence tests
Geometric (arithmetico-geometric) Harmonic Alternating Power Binomial Taylor
Summand limit (term test) Ratio Root Integral Direct comparison Limit comparison Alternating series Cauchy condensation Dirichlet Abel

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] The concept was introduced by Newton in 1665 and detailed in his mathematical treatise, Method of Fluxions.^[3] Newton described any variable that changed its value as a fluent – for example, the velocity of a ball thrown in the air. The derivative of a fluent is known as a fluxion, the main focus of Newton's calculus. A fluent can be found from its corresponding fluxion through integration.^[4]

References

↑ Newton, Sir Isaac (1736) (in en). The Method of Fluxions and Infinite Series: With Its Application to the Geometry of Curve-lines. Henry Woodfall; and sold by John Nourse. https://books.google.com/books?id=WyQOAAAAQAAJ. Retrieved 6 March 2017.
↑ Fluent (mathematics) at the Encyclopædia Britannica
↑ Weisstein, Eric W.. "Fluent". http://mathworld.wolfram.com/Fluent.html.
↑ "Isaac Newton (1642-1727)". http://www.mhhe.com/math/calc/smithminton2e/cd/tools/timeline/newton.html. Retrieved 6 March 2017.

v t e Calculus
Precalculus	Binomial theorem Concave function Continuous function Factorial Finite difference Free variables and bound variables Fundamental theorem Graph of a function Linear function Mean value theorem Radian Rolle's theorem Secant Slope Tangent
Limits	Indeterminate form Limit of a function One-sided limit Limit of a sequence Orders of approximation (ε, δ)-definition of limit
Differential calculus	Chain rule Derivative Differential Differential equation Differential operator Implicit differentiation Inverse functions and differentiation L'Hôpital's rule Leibniz's rule Logarithmic derivative Mean value theorem Newton's method Notation Leibniz's notation Newton's notation Product rule Quotient rule Regiomontanus' angle maximization problem Related rates Simplest rules Constant factor rule in differentiation Linearity of differentiation Power rule Sum rule in differentiation Stationary point First derivative test Second derivative test Extreme value theorem Maxima and minima Taylor's theorem
Integral calculus	Antiderivative Arc length Constant of integration Differentiation under the integral sign Fundamental theorem of calculus Integral of secant cubed Integral of the secant function Integration by parts Integration by substitution Tangent half-angle substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Simplest rules Constant factor rule in integration Linearity of integration Sum rule in integration Trapezoidal rule Trigonometric substitution
Vector calculus	Curl Directional derivative Divergence Divergence theorem Gradient Gradient theorem Green's theorem Laplacian Stokes' theorem
Multivariable calculus	Curvature Disc integration Divergence theorem Exterior Gabriel's Horn Geometric Hessian matrix Jacobian matrix and determinant Line integral Matrix Multiple integral Partial derivative Shell integration Surface integral Tensor Volume integral
Series	Abel's test Alternating Alternating series test Arithmetico-geometric sequence Binomial Cauchy condensation test Direct comparison test Dirichlet's test Euler–Maclaurin formula Fourier Geometric Harmonic Infinite Integral test for convergence Limit comparison test Maclaurin Power Ratio test Root test Taylor Term test
Special functions and numbers	Bernoulli numbers e (mathematical constant) Exponential function Natural logarithm Stirling's approximation
History of calculus	Adequality Brook Taylor Colin Maclaurin Generality of algebra Gottfried Wilhelm Leibniz Infinitesimal Infinitesimal calculus Isaac Newton Fluxion Law of Continuity Leonhard Euler Method of Fluxions The Method of Mechanical Theorems
Lists	Differentiation rules List of integrals of exponential functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of inverse trigonometric functions List of integrals of irrational functions List of integrals of logarithmic functions List of integrals of rational functions List of integrals of trigonometric functions List of limits List of mathematical symbols Lists of integrals

v t e Sir Isaac Newton
Publications	Fluxions (1671) De Motu (1684) Principia (1687; writing) Opticks (1704) Queries (1704) Arithmetica (1707) De Analysi (1711)
Other writings	Quaestiones (1661–65) "standing on the shoulders of giants" (1675) Notes on the Jewish Temple (c. 1680) "General Scholium" (1713; "hypotheses non fingo" ) Ancient Kingdoms Amended (1728) Corruptions of Scripture (1754)
Contributions	Calculus fluxion Impact depth Inertia Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Spectrum Structural coloration
Newtonianism	Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation post-Newtonian expansion parameterized gravitational constant Newton–Cartan theory Schrödinger–Newton equation Newton's laws of motion Kepler's laws Newtonian dynamics Newton's method in optimization Apollonius's problem truncated Newton method Gauss–Newton algorithm Newton's rings Newton's theorem about ovals Newton–Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz–Newton calculus controversy Newton's notation Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method generalized Gauss–Newton method Newton fractal Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number kissing number problem Newton's quotient Parallelogram of force Newton–Puiseux theorem Absolute space and time Luminiferous aether Newtonian series table
Personal life	Woolsthorpe Manor (birthplace) Cranbury Park (home) Early life Later life Religious views Occult studies Scientific Revolution Copernican Revolution
Relations	Catherine Barton (niece) John Conduitt (nephew-in-law) Isaac Barrow (professor) William Clarke (mentor) Benjamin Pulleyn (tutor) John Keill (disciple) William Stukeley (friend) William Jones (friend) Abraham de Moivre (friend)
Depictions	Newton by Blake (monotype) Newton by Paolozzi (sculpture)
Namesake	Isaac Newton Institute Isaac Newton Medal Isaac Newton Telescope Isaac Newton Group of Telescopes Newton (unit)
Categories	Category Isaac Newton not found

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