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:

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