Titlebook: Nonstandard Analysis in Practice; Francine Diener,Marc Diener Textbook 1995 Springer-Verlag Berlin Heidelberg 1995 Martingale.Riemannian g

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Ige326

Tutorial,g the 19th century is a consequence of an idea of E. Nelson [91]: to resort to an adjective, the predicate ., which is deliberately left undefined. This idea makes it possible to dissociate completely the logical foundation of the nonstandard method from its practical use.

capillaries

Neutrices, external numbers, and external calculus,e, have developed formalisms which start by defining the notion of order of magnitude of a function and then give rules which allow some elementary calculations using this notion. The notation of Landau is perhaps a good example. (See [93].) We also mention the “Infinitärcalcül” of Du Bois-Reymond. (See [68].)

concert

The Vibrating String,y notion of functional spaces. This example is very simple, but it is interesting because it can be generalised. The generally used theory represents the string position at the point ., at the time ., by a continuous function .(.), with . and . real. This function is a solution of the equations (PDE):

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Complex analysis,ifficulty, as though you had to fly a Concorde ! Briefly, complex analysis gives complexes. Otherwise excellent courses on complex analysis do not clearly answer the first question one might be tempted to ask: what does an analytic function look like. And, finally, too much information prevents a good understanding of complex analysis.

Choreography

Integration over finite sets,aces. It is known that any situation can be reduced to this one. For example [32], in order to integrate a function over an interval . of ℝ, we consider a finite approximation of . i.e. a finite partition . = (.)o≤.≤. of ., infinitesimally fine (which we call a near interval) and we define the integral of . as the finite sum.