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Laplace Transforms
The Laplace transform of a function f(t) produces a function F(s) in the image
domain that can be utilized to find the solution of a linear differential equation
involving f(t) through algebraic methods. The steps involved in this
application are three:
1. Use of the Laplace transform converts the linear ODE involving f(t) into an
algebraic equation.
2. The unknown F(s) is solved for in the image domain through algebraic
manipulation.
3. An inverse Laplace transform is used to convert the image function found
in step 2 into the solution to the differential equation f(t).
Laplace transform and inverses in the calculator
The calculator provides the functions LAP and ILAP to calculate the Laplace
transform and the inverse Laplace transform, respectively, of a function f(VX),
where VX is the CAS default independent variable (typically X). The
calculator returns the transform or inverse transform as a function of X. The
functions LAP and ILAP are available under the CALC/DIFF menu. The
examples are worked out in the RPN mode, but translating them to ALG mode
is straightforward.
Example 1
– You can get the definition of the Laplace transform use the
following: ‘
’ in RPN mode, or in ALG mode.
The calculator returns the result (RPN, left; ALG, right):
Compare these expressions with the one given earlier in the definition of the
Laplace transform, i.e.,
∞
−
⋅==
0
,)()()}({ dtetfsFtf
st
L