# A report on Mathematical analysis, Calculus and Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy (, ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics.

- Augustin-Louis CauchyHe was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors.

- Augustin-Louis CauchyAnalysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

- Mathematical analysisIn mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.

- CalculusIn 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, particularly by Euler.

- Mathematical analysisSeveral mathematicians, including Maclaurin, tried to prove the soundness of using infinitesimals, but it would not be until 150 years later when, due to the work of Cauchy and Weierstrass, a way was finally found to avoid mere "notions" of infinitely small quantities.

- Calculus1 related topic with Alpha

## Limit of a function

0 linksNot defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

Not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.

In his 1821 book Cours d'analyse, Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of y=f(x) by saying that an infinitesimal change in x necessarily produces an infinitesimal change in y, while claims that he used a rigorous epsilon-delta definition in proofs.