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

See also

First Order (disambiguation) Original order, the first ordering