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
Other uses
- First-order desire
- First-order election, in political science, the relative importance of certain elections
- First order Fresnel lens
