Bhaskara II, also known as Bhaskaracharya, was an Indian mathematician and astronomer who lived in the 12th century. He is credited with discovering 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 a point where the value of the function is equal to the average value of the function on the closed interval.

Madhava of Sangamagrama, who lived in the 14th century, is considered to be the first mathematician to develop the concept of the differential coefficient. He used this concept to derive series expansions for various functions, including the sine and cosine functions.

Indian mathematicians made significant contributions to the development of calculus. They developed the concept of the derivative, discovered the fundamental theorem of calculus, and applied calculus to solve real-world problems in astronomy, engineering, and other fields.

Indian mathematicians have made significant contributions to the field of artificial intelligence by applying calculus to develop algorithms for machine learning, create models for natural language processing, and design computer vision systems.

Lagrange, a French mathematician of Indian origin, made significant contributions to the calculus of variations. He developed the method of Lagrange multipliers, which is a powerful tool for solving constrained optimization problems.

Indian mathematicians made significant contributions to the field of numerical analysis by developing methods for solving linear equations, discovering algorithms for interpolation and approximation, and applying numerical analysis to solve problems in physics and engineering.

Indian mathematicians have used calculus to make significant contributions to the development of algorithms for machine learning by optimizing the parameters of machine learning models, deriving learning rules for neural networks, and analyzing the convergence properties of machine learning algorithms.

Srinivasa Ramanujan, who lived in the early 20th century, was a brilliant Indian mathematician who made significant contributions to the theory of numbers. He discovered many remarkable identities and formulas related to prime numbers, modular forms, and other topics.

Indian mathematicians have used calculus to make significant contributions to the creation of models for natural language processing by analyzing the structure of natural language, developing algorithms for machine translation, and designing natural language understanding systems.

Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, made significant contributions to the theory of relativity. He is known for his work on white dwarf stars and the Chandrasekhar limit, which is the maximum mass that a white dwarf star can have before it collapses under its own gravity.

Indian mathematicians have used calculus to make significant contributions to the design of computer vision systems by developing algorithms for image processing, creating models for object recognition, and designing systems for motion tracking.

C. V. Raman, an Indian physicist, made significant contributions to the study of the Navier-Stokes equations, which describe the motion of fluids. He is known for his work on the scattering of light by molecules, which is known as the Raman effect.

Indian mathematicians applied calculus to solve real-world problems in astronomy by calculating the orbits of planets and moons, determining the distance to stars and galaxies, and modeling the evolution of the universe.

Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, made significant contributions to the theory of black holes. He is known for his work on the Chandrasekhar limit, which is the maximum mass that a white dwarf star can have before it collapses under its own gravity and becomes a black hole.

Indian mathematicians applied calculus to solve real-world problems in engineering by designing bridges and buildings, analyzing the forces acting on structures, and optimizing the performance of machines.