Why Mañjula Matters
From The Laghumānasa of Mañjula — the Dawn of Calculus, taught by Acharya T Krishnatrey. This lesson is free to read.
<pre data-block="research">Historians of mathematics cite Mañjula (Muñjāla) for the early statement — in his Laghumānasa (III.14) — of the koṭijyā "motion-correction", which reads as sin w′ − sin w = (w′ − w) cos w, an explicit differential of the sine used in his lunar theory. His Laghumānasa was a widely used practical handbook (karaṇa). Together with Bhāskara II's instantaneous-velocity work and the Kerala school's infinite series, Mañjula is part of the documented evidence that key ideas of the calculus were developed in India well before their European formulation.</pre>