Sentence examples for infinitesimal analysis from inspiring English sources

The first calculus textbook was also due to Johann his lecture notes Analyse des infiniment petits ("Infinitesimal Analysis") was published by the marquis de l'Hôpital in 1696 and calculus in the next century was dominated by his great Swiss student Leonhard Euler, who was invited to Russia by Catherine the Great and thus helped to spread the Leibniz doctrine to all corners of Europe.

For myself this feeling of dissatisfaction was so overpowering that I made a fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis.…I succeeded on November 24 , 1858

Peano's Calcolo differenziale e principii di calcolo integrale (1884; "Differential Calculus and Principles of Integral Calculus") and Lezioni di analisi infinitesimale, 2 vol. (1893; "Lessons of Infinitesimal Analysis"), are two of the most important works on the development of the general theory of functions since the work of the French mathematician Augustin-Louis Cauchy (1789 1857).

In 1889 Bertrand's research on infinitesimal analysis led to his important work, Calcul des probabilités ("Calculus of Probabilities"), which introduced the problem known as Bertrand's paradox concerning the probability that a "random chord" of a circle will be shorter than its radius.

The "internal" logic of smooth infinitesimal analysis is accordingly not full classical logic.

For an elementary account of smooth infinitesimal analysis see Bell (1998).

We use Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm.

Based on Infinitesimal Perturbation Analysis, the developed technique retrieves information on throughput gradient with respect to system parameters.

Infinitesimal perturbation analysis (IPA) provides formulas for random gradients (derivatives) of performance measures with respect to parameters of interest, computed from sample paths of stochastic systems.

By exploiting Infinitesimal Perturbation Analysis to capture the network performance sensitivity, we obtain an adaptive control law suitable for on-line control on the basis of traffic samples acquired during the network evolution.

The gain is computed in real time by infinitesimal perturbation analysis, and the resultant control system displays wide stability margins as well as considerable robustness to modeling and computing errors.