Indian Contributions to the Applications of Calculus

Madhava of Sangamagrama, who lived in the 14th century, is credited with developing the concept of the Taylor series and using it to approximate the values of trigonometric functions.

The Taylor series is a series expansion of a function in terms of its derivatives at a particular point.

Lagrange, who was born in Italy but spent a significant portion of his life in India, made important contributions to the calculus of variations, a branch of mathematics that deals with finding the extrema of functionals.

Ramanujan's summation formula is a series expansion for pi that converges very rapidly.

Srinivasa Ramanujan, who lived in the early 20th century, made significant contributions to the theory of numbers, including the discovery of new prime number patterns and the development of new methods for solving Diophantine equations.

Ramanujan's modular equation is a deep and beautiful result that connects two seemingly unrelated areas of mathematics: number theory and modular forms.

Harish-Chandra, who lived in the 20th century, made significant contributions to the theory of functions, including the development of new methods for classifying and representing representations of Lie groups.

Harish-Chandra's character formula is a fundamental result in the theory of representations of Lie groups.

Subrahmanyan Chandrasekhar, who lived in the 20th century, made significant contributions to the theory of differential equations, including the development of new methods for solving partial differential equations.

Chandrasekhar's mass-luminosity relation is a fundamental result in astrophysics that relates the mass of a star to its luminosity.

C. R. Rao, who is still alive today, has made significant contributions to the theory of probability, including the development of new methods for statistical inference.

Rao's inequality is a fundamental result in statistics that provides a lower bound on the variance of an estimator.

Narayana Murthy, who is still alive today, has made significant contributions to the theory of optimization, including the development of new algorithms for solving linear and nonlinear programming problems.

Murthy's simplex method is a variant of the simplex method for solving linear programming problems that is known for its efficiency and robustness.

Pradeep Khosla, who is still alive today, has made significant contributions to the theory of control, including the development of new methods for designing and analyzing control systems.

Khosla's stability theorem is a fundamental result in control theory that provides a necessary and sufficient condition for the stability of a control system.