convert/Heaviside - Maple Programming Help

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convert/Heaviside

Convert a piecewise function to a Heaviside expression

 

Calling Sequence

Parameters

Description

Examples

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

convertpiecewise0<x&comma;1&comma;Heaviside

Heavisidex

(1)

convertpiecewisex<0&comma;1&comma;x<1&comma;2&comma;x<2&comma;3&comma;Heaviside

1&plus;Heavisidex&plus;Heaviside1&plus;x3Heaviside2&plus;x

(2)

convertx&comma;Heaviside

x&plus;2xHeavisidex

(3)

convertHeavisidexa&comma;Heaviside&comma;positivex

Heavisidexa

(4)

convertHeavisidexa&comma;Heaviside&comma;positivea

1Heavisidex&plus;a

(5)

See Also

convert/piecewise

piecewise

 


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