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)

Look up first-order in Wiktionary, the free dictionary.

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

See also

Search for "first-order" on Wikipedia.

All pages with titles containing First-order or First-orders
All pages with titles beginning with First Order
All pages with titles beginning with First-order
First Order (disambiguation)
Original order, the first ordering
First (disambiguation)
Order (disambiguation)

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