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Mathematical analysis is the broad branch of mathematics that dealing with limits and related theories, such as differentiation, integration, measure, infinite series and analytic functions.
Mathematical analysis is includes a very large part of mathematics and we can subdivide these analysis into Real analysis and Complex analysis.
In simplest form, mathematical analysis is the study of the theory behind calculus. In calculus, we learns how to calculate things like derivatives, integrals and measure. and in analysis, we learns why these calculations are correct, how to prove they are correct, and how to take hand-wavey definitions of things.
It include the theory of differential calculus, the theory of integral calculus, the theory of functions of a real variable, the theory of functions of a complex variable, the theory of approximation theory, the theory of ordinary differential equations, the theory of partial differential equations, the theory of integral equations, differential geometry, variational calculus, functional analysis, harmonic analysis, and certain other mathematical disciplines.
Modern number theory and probability theory use and develop methods of mathematical analysis.
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