{{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: {{TOC right}}
== 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 == * 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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