first-order

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In mathematics and other formal sciences, first-order or first order most often means either:

"linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
"without self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic)

In detail, it may refer to:

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Mathematics

First-order approximation
First-order arithmetic
First-order condition
First-order hold, a mathematical model of the practical reconstruction of sampled signals
First-order inclusion probability
First Order Inductive Learner, a rule-based learning algorithm
First-order reduction, a very weak type of reduction between two computational problems
First-order resolution
First-order stochastic dominance
First order stream

= Differential equations =

Exact first-order ordinary differential equation
First-order differential equation
First-order differential operator
First-order linear differential equation
First-order non-singular perturbation theory
First-order partial differential equation, a partial differential equation that involves only first derivatives of the unknown function of n variables
Order of accuracy

= Logic =

First-order language
First-order logic, a formal logical system used in mathematics, philosophy, linguistics, and computer science
First-order predicate, a predicate that takes only individual(s) constants or variables as argument(s)
First-order predicate calculus
First-order theorem provers
First-order theory
Monadic first-order logic

Chemistry

First-order fluid, another name for a power-law fluid with exponential dependence of viscosity on temperature
First-order reaction, a first-order chemical reaction
First-order transition

Computer science

Other uses

First-order desire
First-order election, in political science, the relative importance of certain elections
First order Fresnel lens
First order (religious), an institute of consecrated life for men
First Order of Saint Francis, one such grouping
First Order (Star Wars), a fictional autocratic military dictatorship

See also

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Original order, the first ordering

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