Continuous functions, convergences, and limits can combine into one subject {functional analysis}. Analysis includes infinite series, ordinary differential equations, partial differential equations, differential geometry, calculus, and calculus of variations. Analysis excludes plane geometry, solid geometry, and computational methods. Analysis uses arithmetic, variable, function, continuity, differentiability, integrability, limits, infinitesimals, infinite, least upper bound, uniformity, convergence, and fundamental theorem of calculus.
purposes
Functional analysis can be for generalized moment problem, statistical mechanics, fixed-point theorems, partial-differential-equation existence and uniqueness theorems, calculus of variations, and continuous compact-group representation. Linear functional analysis can study integral equations.
functional
Functions of functions {functional} map function to number. Functionals can find areas of products of two functions, over intervals. Functionals can evaluate functions at points. Functionals have generalized derivatives that are also functionals, but can have singularities.
Mathematical Sciences>Calculus>Analysis>Kinds
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Date Modified: 2022.0224