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
gollark: I didn't actually say that. I'm not sure what you're agreeing with.
gollark: No, I mean you said you would ignore metadiscussion outside it.
gollark: You could express opinions and discuss things *anyway*, see.
gollark: It's a slightly different discussion channel with more constraints. It isn't particularly amazing as an innovation, and it enforces a style of communication you prefer and some don't on pain of being ignored (more).
gollark: You are assuming that people actually all thought of it as a good thing in the same way.

See also

  • 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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