First-order

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title: "First-order" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public topic_path: "uncategorized" source: "https://en.wikipedia.org/wiki/First-order" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

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:

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

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