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Newton provided some of the most important applications to physics, especially of integral calculus. The purpose of this section is to examine Newton and Leibniz’s investigations into the developing field of infinitesimal calculus. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness… In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa… Εάν η ταχύτητα είναι σταθερή, απαιτείται μόνο πολλαπλασιασμός, αλλά αν μεταβληθεί η ταχύτητα, τότε χρειαζόμαστε μια πιο ισχυρή μέθοδος για την εξεύρεση της απόστασης.

Nevertheless, it is possible to check that the conclusion of Stokes' theorem is still true. This is because Ω and its boundary are well-behaved away from a small set of points (a measure zero set).

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It is named after Gabriel Cramer (1704–1752), who published the rule for an arbitrary number of unknowns in 1750, although Colin Maclaurin also published special cases of the rule in 1748 (and possibly knew of it as early as 1729)..

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When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today…