Indian Contributions to the Foundations of Calculus

Madhava of Sangamagrama (c. 1340-1425) is credited with developing the concept of the derivative, which is a fundamental concept in calculus.

The Madhava series is a series used to approximate the value of pi. It was developed by Madhava of Sangamagrama in the 14th century.

Bhaskara II (1114-1185) developed the concept of the integral, which is another fundamental concept in calculus.

Bhaskara II used the exhaustion method to calculate the area of a curved surface. This method involves dividing the surface into a large number of small pieces and then finding the sum of the areas of these pieces.

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the limit, which is a fundamental concept in calculus.

Rolle's theorem states that the derivative of a function is equal to the slope of the tangent line to the graph of the function at a given point.

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the chain rule, which is a fundamental concept in calculus.

The fundamental theorem of calculus states that the integral of a function is equal to the area under the curve of the function.

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the inverse function, which is a fundamental concept in calculus.

The inverse function theorem states that the derivative of an inverse function is equal to the reciprocal of the derivative of the original function.

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the logarithmic function, which is a fundamental concept in calculus.

The logarithmic differentiation theorem states that the derivative of a logarithmic function is equal to the reciprocal of the function.

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the exponential function, which is a fundamental concept in calculus.

The exponential differentiation theorem states that the derivative of an exponential function is equal to the function itself.

Aryabhata (476-550) developed the concept of the trigonometric functions, which are fundamental concepts in calculus.