Manual HP 49g graphing calculator (page 149 of 175) (English)

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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: ‘f(X)’ ` L P 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.,

∫

∞

−

⋅==

,)()()}({ dtetfsFtf

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HP 49g graphing calculator Manual

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