title: First-order
text: # 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
  