Indian Mathematicians and their Contributions to Calculus

Madhava of Sangamagrama, also known as Madhavacharya, is widely regarded as the "Father of Indian Calculus" for his significant contributions to the development of calculus in the 14th century.

Madhava of Sangamagrama developed the Madhava Series, also known as the Madhava-Gregory Series, to approximate the value of (\pi). This series is a precursor to the Taylor Series and Maclaurin Series.

Brahmagupta, an Indian mathematician and astronomer, is renowned for his contributions to indeterminate equations and the development of the chakravala method, a cyclic algorithm for solving indeterminate equations.

Bhaskara I, also known as Bhaskaracharya, is credited with the discovery of the Rolle's Theorem, which states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the derivative is zero.

Nilakantha Somayaji, an Indian mathematician and astronomer, developed the concept of the mean value theorem, which states that for a function that is continuous on a closed interval and differentiable on the open interval, there exists at least one point in the open interval where the derivative is equal to the average rate of change of the function over the closed interval.

Madhava of Sangamagrama made significant contributions to the study of infinite series and is credited with the development of the Taylor Series, which is a powerful tool for approximating the value of a function at a given point.

Brahmagupta, in addition to his contributions to indeterminate equations, is also known for his work on continued fractions. He developed a method for expressing the square root of a non-perfect square as a continued fraction.