An Introduction to Non-Standard Analysis and its Applications
نویسنده
چکیده
When Newton and Leibnitz practiced calculus, they used infinitesimals, which were supposed to be like real numbers, yet of smaller magnitude than any other type of postive real number. In the 19th century, mathematicians realized they could not justify the use of infinitesimals according to their sense of rigor, so they began using definitions involving ’s and δ’s. Then, in the early 1960’s, the logician Abraham Robinson figured out a way to rigorously define infinitesimals, creating a subject now known as nonstandard analysis.
منابع مشابه
An Introduction to Speech Sciences (Acoustic Analysis of Speech)
Speech sciences deal with the acoustical characteristics of speech by means of sophisticated soft wares as well as hard wares. Although, a speech science is a well known science in the developed countries, especially the western societies, however, it has been remained almost unknown in Iran, though, in recent years a group of scholars have been involved in this branch of science. The applicati...
متن کاملExternal and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملModification of Displacement Coefficient Method in Estimation of Target Displacement for Regular Concrete Bridges Based on ASCE 41-06 Standard
Displacement Coefficient Method (DCM) stipulated in the ASCE 41-06 standard is becoming the preferred method for seismic rehabilitation of buildings in many high-seismic-hazard countries. Applications of the method for non-building constructions such as bridges are beyond the scope of this standard. Thus its application to this kind of structure should be approached with care. Target displaceme...
متن کاملSynchrosqueezing-based Transform and its Application in Seismic Data Analysis
Seismic waves are non-stationary due to its propagation through the earth. Time-frequency transforms are suitable tools for analyzing non-stationary seismic signals. Spectral decomposition can reveal the non-stationary characteristics which cannot be easily observed in the time or frequency representation alone. Various types of spectral decomposition methods have been introduced by some resear...
متن کاملAPPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN STABILITY INDEX AND CRITICAL LENGTH IN AVALANCHE DYNAMICS
In this study, Stability analysis of snow slab which is under detonation has developed in the present model. The model has been studied by using the basic concepts of non-detonation model and concepts of underwater explosions with appropriate modifications to the present studies. The studies have also been extended to account the effect of critical length variations at the time of detonation an...
متن کاملRobust Wagner–Whitin algorithm with uncertain costs
In real-world applications, costs for products are not deterministic: neither static nor dynamic. They actually tend to be non-stationary and cross-correlated. To overcome this drawback, there have been some efforts by researchers to extend the Wagner–Whitin algorithm to consider stochastic costs. However, they assume that the information of probability density function of random costs exists. ...
متن کامل