mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and other

formal sciences Formal science is a Branches of science, branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, inform ...

, first-order or first order most often means either: * "

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

" (a polynomial of degree at most one), as in

first-order approximation In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. Usage in science and engineering In formal expressions, the ordinal number used ...

and other calculus uses, where it is contrasted with "polynomials of higher degree", or * "without self-reference", as in

first-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...

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 In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. Usage in science and engineering In formal expressions, the ordinal number used ...

First-order arithmetic In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their properties. Preliminaries For every natural mathematical structure ...

First-order condition In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information abou ...

* 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 In computer science, a first-order reduction is a very strong type of reduction between two computational problems in computational complexity theory. A first-order reduction is a reduction where each component is restricted to be in the class FO ...

, a very weak type of reduction between two computational problems *

First-order resolution In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically ...

* First-order stochastic dominance * First order stream

Differential equations

* Exact first-order ordinary differential equation *

First-order differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives ...

First-order differential operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and retur ...

First-order linear differential equation In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) where and are arbi ...

* First-order non-singular perturbation theory *

First-order partial differential equation In mathematics, a first-order partial differential equation is a partial differential equation that involves the first derivatives of an unknown function u of n\geq 2 variables. The equation takes the form F(x_1,\ldots,x_n,u,u_,\ldots u_) =0, using ...

, a partial differential equation that involves only first derivatives of the unknown function of ''n'' variables *

Order of accuracy In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution. Consider u, the exact solution to a differential equation in an appropriate normed space (V ...

Logic

First-order language First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...

First-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...

, 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 logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...

* First-order theorem provers *

First-order theory In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, giving rise to a formal system that combines the language with deduct ...

* 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 * First order (religious), an institute of consecrated life for men ** First Order of Saint Francis, one such grouping *

First Order (Star Wars) The First Order is a fictional military movement and rump state in the ''Star Wars'' franchise, introduced in the 2015 film ''The Force Awakens''. It is formed following the fall of the Galactic Empire after the events of ''Return of the Jedi ...