Calculus is a branch of mathematics concerned with the study of continuous change. It has two major branches, differential calculus and integral calculus.
Differential calculus is the study of the definition, properties and applications of the derivative of a function, and the process of finding the derivative is called differentiation. Given a function and a point in the domain, the derivative is a way of encoding small-scale behaviour of the function near that point. By finding the derivative of a function at every point in its domain, it’s possible to produce a new function or the derivative function as it is called. The derivative is a linear operator, which functions as its input and produces a second function as its output.
Integral calculus is the study of definitions, properties and applications of two related concepts, both called the indefinite and definite integral. Finding the value of an integral is used for a process called integration – integral calculus studies, two related linear operators. Known as the anti-derivative, the indefinite integral is the inverse operation to the derivative.
On the other hand, mathematical analysis evolved from calculus and deals with limits and is concerned with theories such as differentiation, integration, infinite series, analytic functions and measure. They are usually studied in the context of real and complex numbers and functions.
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