First-order
# 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
