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**Functional Analysis Introduction **

Functional analysis is a branch of mathematical analysis, that deals with the theory of vector spaces and linear functionals. Its dealing with functionals, or functions of functions.

Functional analysis plays an important role in the applied sciences such as ordinary and partial differential equations, numerical analysis, calculus of variations, theory of measure, approximation theory, integral equations, probability to infinite dimensional spaces (infinite dimensional analysis) and so on.

Functional analysis is usually an extension of linear algebra, usually linear spaces, usually spaces of functions and usually infinite dimensional.

It looks at spaces with more structure than just a vector space. In order of increasing structure there’s at least a topology (such as Fréchet spaces), often a norm (Banach spaces), and sometimes an inner product (Hilbert spaces)

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