Hp 50g Graphing Calculator Manual de usuario descargar pdf (Pagina 488)

100

101

Page 16-11

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, which you should set to ‘X’.

Thus, 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. For these examples, set the CAS mode to Real and Exact.

Example 1

– You can get the definition of the Laplace transform use the

following: ‘f(X)’ ` LP in RPN mode, or L P(f(X))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.,

and you will notice that the CAS default variable X in the equation writer screen

replaces the variable s in this definition. Therefore, when using the function

LAP you get back a function of X, which is the Laplace transform of f(X).

Example 2

– Determine the Laplace transform of f(t) = e

⋅sin(t). Use:

‘EXP(2*X)*SIN(X)’ ` LAP The calculator returns the result: 1/(SQ(X-2)+1).

Press μ to obtain, 1/(X

-4X+5).

When you translate this result in paper you would write

∫

∞

−

⋅==

,)()()}({ dtetfsFtf

}sin{)(

+⋅−

=⋅=

tesF

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Hp 50g Graphing Calculator Manual de usuario Pagina 488

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