Heaviside - Maple Help

convert/Heaviside

Convert a piecewise function to a Heaviside expression

 Calling Sequence convert( expr, Heaviside ) convert( expr, Heaviside, positive ) convert( expr, Heaviside, positive(var) )

Parameters

 expr - expression containing piecewise positive - literal keyword var - variable for Heaviside sign

Description

 • Converts a piecewise function to an expression with Heaviside functions.
 • If the optional third argument 'positive' is given, then the expression must only depend on one variable, and on output all Heaviside functions with an argument that is linear in that variable will be written so that the sign of the coefficient of that variable, if it can be detected, will be positive.
 When the input depends on more than one variable, the form positive(var) must be used to specify the variable.
 • If the expression contains an abs or a signum, these are also converted to Heaviside expressions.
 • Note that conversion to Heaviside can result in a function which differs from the original in finitely many points.  For this reason, conversion to Heaviside should generally be done prior to definite integration.

Examples

 > $\mathrm{convert}\left(\mathrm{piecewise}\left(0
 ${\mathrm{Heaviside}}{}\left({x}\right)$ (1)
 > $\mathrm{convert}\left(\mathrm{piecewise}\left(x<0,1,x<1,2,x<2,3\right),\mathrm{Heaviside}\right)$
 ${1}{+}{\mathrm{Heaviside}}{}\left({x}\right){+}{\mathrm{Heaviside}}{}\left({-}{1}{+}{x}\right){-}{3}{}{\mathrm{Heaviside}}{}\left({-}{2}{+}{x}\right)$ (2)
 > $\mathrm{convert}\left(\mathrm{abs}\left(x\right),\mathrm{Heaviside}\right)$
 ${-}{x}{+}{2}{}{x}{}{\mathrm{Heaviside}}{}\left({x}\right)$ (3)
 > $\mathrm{convert}\left(\mathrm{Heaviside}\left(x-a\right),\mathrm{Heaviside},\mathrm{positive}\left(x\right)\right)$
 ${\mathrm{Heaviside}}{}\left({x}{-}{a}\right)$ (4)
 > $\mathrm{convert}\left(\mathrm{Heaviside}\left(x-a\right),\mathrm{Heaviside},\mathrm{positive}\left(a\right)\right)$
 ${1}{-}{\mathrm{Heaviside}}{}\left({-}{x}{+}{a}\right)$ (5)