This package can calculate ordinary and inverse Laplace transforms of expressions. Documentation is in plain text.
Authors: C. Kazasov, M. Spiridonova, V. Tomov.
Christomir Kazasov, Laplace Transformations in REDUCE 3, Proc. Eurocal ’87, Lecture Notes in Comp. Sci., Springer-Verlag (1987) 132-133.
Some hints on how to use to use this package:
LAPLACE(< exp >,< var - s >,< var - t > )
INVLAP(< exp >,< var - s >,< var - t >)
where < exp > is the expression to be transformed, < var -s > is the source variable (in most cases < exp > depends explicitly of this variable) and < var -t > is the target variable. If < var - t > is omitted, the package uses an internal variable lp!& or il!&, respectively.
The following switches can be used to control the transformations:
If on, sin, cos, sinh and cosh are converted by LAPLACE into exponentials,
If on, expressions e˜x are converted by INVLAP into hyperbolic functions sinh and cosh,
If on, expressions e˜x are converted by INVLAP into trigonometric functions sin and cos.
The system can be extended by adding Laplace transformation rules for single functions by rules or rule sets. In such a rule the source variable MUST be free, the target variable MUST be il!& for LAPLACE and lp!& for INVLAP and the third parameter should be omitted. Also rules for transforming derivatives are entered in such a form.
Remarks about some functions:
The DELTA and GAMMA functions are known.
ONE is the name of the unit step function.
INTL is a parametrized integral function
intl(< expr >,< var >,0,< obj.var >)
which means "Integral of < expr > wrt. < var > taken from 0 to < obj.var >", e.g.
intl(2*y2,y,0,x) which is formally a function in x.
We recommend reading the file LAPLACE.TST for a further introduction.