Definition, Betydelse & Synonymer | Engelska ordet DIFFERENTIABLE

Definition av DIFFERENTIABLE

1. (matematik, ej komparabelt) deriverbar, differentierbar
2. (komparabelt, med "more" och "most"; om flera föremål) som går att särskilja

Exempel på hur man kan använda DIFFERENTIABLE i en mening

• In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable.
• It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are continuously differentiable.
• There can be functions for which partial derivatives exist in every direction but fail to be differentiable.
• In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space.
• Mathematical singularity, a point at which a given mathematical object is not defined or not "well-behaved", for example infinite or not differentiable.
• The twice continuously differentiable solutions of Laplace's equation are the harmonic functions, which are important in multiple branches of physics, notably electrostatics, gravitation, and fluid dynamics.
• Examples of such spaces are spaces of holomorphic functions on an open domain, spaces of infinitely differentiable functions, the Schwartz spaces, and spaces of test functions and the spaces of distributions on them.
• The notion of closed set is defined above in terms of open sets, a concept that makes sense for topological spaces, as well as for other spaces that carry topological structures, such as metric spaces, differentiable manifolds, uniform spaces, and gauge spaces.
• This is significant because one can then prove Cauchy's integral formula for these functions, and from that deduce these functions are infinitely differentiable.
• Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions.
• In differential geometry, parametric equations are usually assumed to be differentiable (or at least piecewise differentiable).
• Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized and RO can hence be used on functions that are not continuous or differentiable.
• Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule.
• In mathematics, a diffeology on a set generalizes the concept of smooth charts in a differentiable manifold, declaring what the "smooth parametrizations" in the set are.
• Moreover, the rotation group has a natural structure as a manifold for which the group operations are smoothly differentiable, so it is in fact a Lie group.
• Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
• Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensions.
• In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one point, somewhere between them, at which the slope of the tangent line is zero.
• Firstly, if one knows, for example by physical measurement, the values of a function and its derivative at some sampling points, one can interpolate the function with a continuously differentiable function, which is a piecewise cubic function.
• A differentiable function of one variable is convex on an interval if and only if its derivative is monotonically non-decreasing on that interval.

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