Editing History of calculus (section)

====India====
{{see also|Indian mathematics}}
Evidence suggests [[Bhāskara II]] was acquainted with some ideas of differential calculus.<ref>50 Timeless Scientists von K.Krishna Murty</ref> Bhāskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of '[[infinitesimal]]s'.<ref>{{cite journal |last=Shukla |first=Kripa Shankar |year=1984 |title=Use of Calculus in Hindu Mathematics |journal=Indian Journal of History of Science |volume=19 |pages=95–104}}</ref> There is evidence of an early form of [[Rolle's theorem]] in his work, though it was stated without a modern formal proof.<ref>{{Cite web |title=Rolle’s theorem {{!}} Definition, Equation, & Facts {{!}} Britannica |url=https://www.britannica.com/science/Rolles-theorem |access-date=2025-03-02 |website=www.britannica.com |language=en}}</ref><ref>{{cite book |first=Roger |last=Cooke |title=The History of Mathematics: A Brief Course |publisher=Wiley-Interscience |year=1997 |chapter=The Mathematics of the Hindus |pages=[https://archive.org/details/historyofmathema0000cook/page/213 213–215] |isbn=0-471-18082-3 |chapter-url=https://archive.org/details/historyofmathema0000cook/page/213}}</ref> In his astronomical work, Bhāskara gives a result that looks like a precursor to infinitesimal methods: if <math>x \approx y</math> then <math>\sin(y) - \sin(x) \approx (y - x)\cos(y)</math>. This leads to the derivative of the sine function, although he did not develop the notion of a derivative.<ref>{{cite book |first=Roger |last=Cooke |title=The History of Mathematics: A Brief Course |publisher=Wiley-Interscience |year=1997 |chapter=The Mathematics of the Hindus |pages=[https://archive.org/details/historyofmathema0000cook/page/213 213–215] |isbn=0-471-18082-3 |chapter-url=https://archive.org/details/historyofmathema0000cook/page/213}}</ref>

Some ideas on calculus later appeared in Indian mathematics, at the [[Kerala school of astronomy and mathematics]].<ref name=katz/> [[Madhava of Sangamagrama]] in the 14th century, and later mathematicians of the Kerala school, stated components of calculus such as the [[Taylor series]] and [[infinite series]] approximations.<ref>[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian_mathematics.html Indian mathematics<!-- Bot generated title -->]</ref> They considered series equivalent to the Maclaurin expansions of {{tmath|\sin(x)}}, {{tmath|\cos(x)}}, and {{tmath|\arctan(x)}} more than two hundred years before they were studied in Europe. But they did not combine many differing ideas under the two unifying themes of the [[derivative]] and the [[integral]], show the connection between the two, and turn calculus into the powerful problem-solving tool we have today.<ref name=katz/>