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Integration of Piecewise Functions with Applications

Maxim Rytin
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The notebook contains the implementation of four functions PiecewiseIntegrate, PiecewiseSum, NPiecewiseIntegrate, NPiecewiseSum. They are intended for working with piecewise continuous functions, and also generalized functions in the case of PiecewiseIntegrate. They support all the standard Mathematica piecewise functions such as UnitStep, Abs, Max, as well as Floor and other arithmetic piecewise functions. PiecewiseIntegrate supports the multidimensional DiracDelta function and its derivatives. The arguments of the piecewise functions can be non-algebraic and contain symbolic parameters.

Mathematica version 5.0 or higher is required.

*Mathematics > Calculus and Analysis > Calculus

piecewise, Dirac delta function, cylindrical algebraic decomposition, CAD
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piecewise.nb (141.5 KB) - Mathematica Notebook [for Mathematica 5.0]