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 control, when a desired result is attempted by adjusting a scalar (first-order) control
• 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

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

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 (disambiguation)
• First-order transition

Computer science

• First-order abstract syntax
• First order functions
• First order query

Other uses

• First order desires
• First-order elections, a term used by political scientists to rate the relative importance of certain elections
• First order Fresnel lens
• First-order stream in Strahler stream order