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We discuss the work of a brilliant line of Mathematicians who lived incentral Kerala and starting with its founder Madhava (1350 CE) developed whatcan best be described as Calculus and applied it to a class of trigonometricfunctions. We explain, with the example of the expansion of the inverse tanfunction, how they handled integration. Further, they took forward the work ofthe fifth century mathematician Aryabahata (499 CE), worked with differentials,and developed the expansion of the sine and the cosine functions. The work\textit{Yuktibhasa} (circa 1500 CE) which maybe described as the first textbookon Calculus, also describes in detail the evaluation of the area and volume oftrigonometric functions as well as a variety of expansions for $\textit{pi}$.Our treatment is pedagogical and we present exercise problems and invite theenterprising student to try their hands at approximations and integration$\textit{a la}$ the Madhava way.

India and the Calculus of Trigonometric Functions