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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [b] [6] [7] [8] Sometimes, it is called first-order propositional logic [9] to contrast it with System F, but it should not be confused with ...
Its first appearance is in a letter written to Guillaume de l'Hôpital by Gottfried Wilhelm Leibniz in 1695. [2] Around the same time, Leibniz wrote to Johann Bernoulli about derivatives of "general order". [3] In the correspondence between Leibniz and John Wallis in 1697, Wallis's infinite product for π is discussed. Leibniz suggested using ...
In theoretical computer science, the modal μ-calculus (Lμ, L μ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with many modalities) by adding the least fixed point operator μ and the greatest fixed point operator ν, thus a fixed-point logic.
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...
For 0 < q < 1, the series converges to a function F(x) on an interval (0,A] if |f(x)x α | is bounded on the interval (0, A] for some 0 ≤ α < 1. The q-integral is a Riemann–Stieltjes integral with respect to a step function having infinitely many points of increase at the points q j..The jump at the point q j is q j.
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.