Erstenorder

Erstenorder is not a single, universally standardized term in German. In technical writing, the concept is usually expressed as "erste Ordnung" or, when used as a compound noun, "Ersterordnung." The English equivalent is "first order." The exact meaning depends on the discipline, but it generally denotes a primary level, a regime described by first-order relations, or a first-order differential or logical framework.

In mathematics, first order often refers to first-order differential equations, which involve the first derivative of a function. A common example is linear first-order equations of the form y' + p(x)y = q(x). Solutions rely on methods such as integrating factors, and initial value problems specify the solution at a starting point. The term also appears in the context of first-order Taylor approximations, where functions are approximated by linear terms around a point.

In logic and computer science, first-order logic (FOL) uses quantification over individual variables but not over predicates or functions. It includes symbols for relations and functions, logical connectives, and quantifiers (for all, exists). FOL serves as a foundational formalism for mathematics and theoretical computer science, distinguishing itself from higher-order logics that quantify over predicates or sets.

In physics and thermodynamics, a first-order phase transition is characterized by a discontinuous change in a system’s first derivatives of the free energy, such as entropy or volume, and is typically accompanied by latent heat. In chemistry and kinetics, first-order processes have rate laws directly proportional to a single reactant’s concentration, yielding exponential decay with half-life t1/2 = ln 2 / k.

In control theory and systems science, a first-order system is described by a single dominant time constant τ, with a standard transfer function of the form K/(τs + 1). Its response to inputs approaches steady state exponentially.