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{{wiktionary|first-order}}
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]]
* [[Strahler stream order|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
* [[Rate equation#First order|First-order reaction]], a first-order chemical reaction
* [[First-order transition]]

== Computer science ==
* [[First-order abstract syntax]]
* [[First-order function]]
* [[First-order query]]

== Other uses ==
* [[First-order desire]]
* [[First-order election]], in political science, the relative importance of certain elections
* [[First order Fresnel lens]]

==See also==
{{canned search|first-order}}
*{{in title|plural=yes}}
*{{lookfrom|First Order}}
*{{lookfrom}}
* [[First Order (disambiguation)]]
* [[Original order]], the first ordering

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