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Change and continuity is a classic dichotomy within the fields of history, historical sociology, and the social sciences more broadly. The question of change and continuity is considered a classic discussion in the study of historical developments. [ 1 ]
A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy defined continuity of = as follows: an infinitely small increment of the independent variable x always produces an infinitely small change (+) of the dependent variable y (see e.g. Cours d'Analyse, p. 34).
A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.
In his 1821 book Cours d'analyse, Augustin-Louis Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of = by saying that an infinitesimal change in x necessarily produces an infinitesimal change in y, while Grabiner claims that he used a rigorous epsilon-delta definition in proofs. [2]
The second term of the right-hand side is the convective rate of change and expresses the contribution of the particle changing position in space (motion). Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field.
Continuity editing, a form of film editing that combines closely related shots into a sequence highlighting plot points or consistencies Continuity (fiction) , consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun)
Continuity and Change is an international peer-reviewed academic journal published three times per year by Cambridge University Press. The journal was established by Richard Wall and Lloyd Bonfield with the intention of defining the field of historical sociology .
The concept of probability current is also used outside of quantum mechanics, when dealing with probability density functions that change over time, for instance in Brownian motion and the Fokker–Planck equation. [1] The relativistic equivalent of the probability current is known as the probability four-current.