Can someone give me an example of a mathematical field in which functional analysis is a prerequisite?!
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1Operator theory – Rick Sanchez Apr 20 '16 at 21:16
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1Partial differential equations, at the graduate level. – hardmath Apr 20 '16 at 22:14
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The study of distributions or generalized functions uses functional analysis heavily. Generalized functions have application in the field of differential equations (finding weak solutions) and is sometimes referred to as "the completion of differential calculus." Distribution theory extends differential calculus in an analogous way to how Lebesgue integration theory extended the theory of integration.
Results from functional analysis can also be used to simplify many proofs in ordinary differential equations.
Merkh
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