Editing Mathematical analysis (section)

====Foundations====
The modern foundations of mathematical analysis were established in 17th century Europe.<ref name=analysis/> This began when [[Fermat]] and [[Descartes]] developed [[analytic geometry]], which is the precursor to modern calculus. Fermat's method of [[adequality]] allowed him to determine the maxima and minima of functions and the tangents of curves.<ref name=Pellegrino>{{cite web | last = Pellegrino | first = Dana | title = Pierre de Fermat | url = http://www.math.rutgers.edu/~cherlin/History/Papers2000/pellegrino.html | access-date = 2008-02-24 | archive-date = 2008-10-12 | archive-url = https://web.archive.org/web/20081012024028/http://www.math.rutgers.edu/~cherlin/History/Papers2000/pellegrino.html | url-status = live }}</ref> Descartes's publication of ''[[La Géométrie]]'' in 1637, which introduced the [[Cartesian coordinate system]], is considered to be the establishment of mathematical analysis. It would be a few decades later that [[Isaac Newton|Newton]] and [[Gottfried Leibniz|Leibniz]] independently developed [[infinitesimal calculus]], which grew, with the stimulus of applied work that continued through the 18th&nbsp;century, into analysis topics such as the [[calculus of variations]], [[Ordinary differential equation|ordinary]] and [[partial differential equation]]s, [[Fourier analysis]], and [[generating function]]s. During this period, calculus techniques were applied to approximate [[discrete mathematics|discrete problems]] by continuous ones.