Differential and Integral Calculus
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Differential calculus: The part of mathematics that develops from the definition of the derivative of a function or the gradient of a graph. The derivative is obtained as the limit of the Newton quotient, and this is equivalent to the notion of the gradient of a graph as the limit of the gradient of a chord of the graph.
Integral calculus: The subject that arose from the problem of trying to find the area of a region with a curved boundary. In general, this is calculated by a limiting process that yields gradually better approximations to the value. The integral is defined by a limiting process based on an intuitive idea of the area under a curve; the fundamental discovery was the link that exists between this and the differential calculus.