# First-order

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> Source revision: 1315314921
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{{wiktionary|first-order}}
In [mathematics](/source/mathematics) and other [formal sciences](/source/formal_sciences), '''first-order''' or '''first order''' most often means either:
* "[linear](/source/linear)" (a polynomial of degree at most one), as in [first-order approximation](/source/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](/source/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](/source/First-order_approximation)
* [First-order arithmetic](/source/First-order_arithmetic)
* [First-order condition](/source/First-order_condition)
* [First-order hold](/source/First-order_hold), a mathematical model of the practical reconstruction of sampled signals
* [First-order inclusion probability](/source/First-order_inclusion_probability)
* [First Order Inductive Learner](/source/First_Order_Inductive_Learner), a rule-based learning algorithm
* [First-order reduction](/source/First-order_reduction), a very weak type of reduction between two computational problems
* [First-order resolution](/source/First-order_resolution)
* [First-order stochastic dominance](/source/First-order_stochastic_dominance)
* [First order stream](/source/Strahler_stream_order)

=== Differential equations ===
* [Exact first-order ordinary differential equation](/source/Exact_first-order_ordinary_differential_equation)
* [First-order differential equation](/source/First-order_differential_equation)
* [First-order differential operator](/source/First-order_differential_operator)
* [First-order linear differential equation](/source/First-order_linear_differential_equation)
* [First-order non-singular perturbation theory](/source/First-order_non-singular_perturbation_theory)
* [First-order partial differential equation](/source/First-order_partial_differential_equation), a partial differential equation that involves only first derivatives of the unknown function of ''n'' variables
* [Order of accuracy](/source/Order_of_accuracy)

=== Logic ===
* [First-order language](/source/First-order_language)
* [First-order logic](/source/First-order_logic), a formal logical system used in mathematics, philosophy, linguistics, and computer science
* [First-order predicate](/source/First-order_predicate), a predicate that takes only individual(s) constants or variables as argument(s)
* [First-order predicate calculus](/source/First-order_predicate_calculus)
* [First-order theorem provers](/source/First-order_theorem_provers)
* [First-order theory](/source/First-order_theory)
* [Monadic first-order logic](/source/Monadic_first-order_logic)

== Chemistry ==
* [First-order fluid](/source/First-order_fluid), another name for a power-law fluid with exponential dependence of viscosity on temperature
* [First-order reaction](/source/Rate_equation), a first-order chemical reaction
* [First-order transition](/source/First-order_transition)

== Computer science ==
* [First-order abstract syntax](/source/First-order_abstract_syntax)
* [First-order function](/source/First-order_function)
* [First-order query](/source/First-order_query)

== Other uses ==
* [First-order desire](/source/First-order_desire)
* [First-order election](/source/First-order_election), in political science, the relative importance of certain elections
* [First order Fresnel lens](/source/First_order_Fresnel_lens)

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

{{SIA}}

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Adapted from the Wikipedia article [First-order](https://en.wikipedia.org/wiki/First-order) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/First-order?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.