mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and other

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

, first-order or first order most often means either: * "linear" (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 b ...

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 known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

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 b ...

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 about ...

First-order hold First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructe ...

, a mathematical model of the practical reconstruction of sampled signals *

First-order inclusion probability In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the draw ...

* 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 whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...

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 return ...

First-order linear differential equation In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b( ...

* 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 only first derivatives of the unknown function of ''n'' variables. The equation takes the form : F(x_1,\ldots,x_n,u,u_,\ldots u_) =0. \, ...

, 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 vector spac ...

Logic

First-order language First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

First-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

, a formal logical system used in mathematics, philosophy, linguistics, and computer science *

First-order predicate In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s).. Compare second-order predicate and higher-order predicate. This is not to be confused with a one-place predicate o ...

, a predicate that takes only individual(s) constants or variables as argument(s) *

First-order predicate calculus First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quan ...

First-order theorem provers Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a maj ...

First-order theory First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantif ...

Monadic first-order logic In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbo ...

Chemistry

First-order fluid A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature. :\mu_\mathrm(\dot \gamma, T) = \mu_0 ^ \exp (-bT) where ''γ̇'' is the shear rate In physics, shear rate is the rate at wh ...

, another name for a power-law fluid with exponential dependence of viscosity on temperature *

First-order reaction In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial react ...

a first-order chemical reaction *

First-order transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

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 *