First-order

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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 control, when a desired result is attempted by adjusting a scalar (first-order) control
• 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

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

See also

• First-order stream in Strahler stream order
• First Order (Star Wars), the principal antagonists in the Star Wars sequel trilogy