Contributions of Indian Mathematicians to Differential Calculus

Aryabhata is widely regarded as the father of Indian mathematics due to his significant contributions to the field, including the development of the decimal system and the concept of zero.

Madhava of Sangamagrama is credited with discovering the fundamental theorem of calculus, which establishes a connection between differentiation and integration.

Madhava of Sangamagrama developed the Madhava series, also known as the Gregory series, which provides an approximation for the value of π.

Bhaskara II developed a method for finding the area of a circle using integration, which involves dividing the circle into small sectors and approximating the area of each sector as a triangle.

Madhava of Sangamagrama is renowned for his work on infinitesimals and the development of calculus techniques, including the use of infinite series to approximate functions.

Bhaskara II developed a method for solving differential equations, which involved using a series of approximations to find the solution.

Bhaskara II developed a method for finding the volume of a sphere using integration, which involves dividing the sphere into small pyramids and approximating the volume of each pyramid as a cone.

Madhava of Sangamagrama developed a method for finding the area of an ellipse using integration, which involves dividing the ellipse into small sectors and approximating the area of each sector as a triangle.

Bhaskara II developed a method for finding the volume of a pyramid using integration, which involves dividing the pyramid into small prisms and approximating the volume of each prism as a cylinder.

Madhava of Sangamagrama developed a method for finding the area of a parabola using integration, which involves dividing the parabola into small sectors and approximating the area of each sector as a triangle.