Casio fx-CP400 - Page 63

Chapter 2: Main Application 63
Syntax:
laplace(
f ( t), t, s)
f ( t): expression ;
t: variable with respect to which the expression is
transformed ;
s: parameter of the transform
invLaplace(
L(s), s, t)
L(s): expression ;
s: variable with respect to which the expression is
transformed ;
t: parameter of the transform
ClassPad supports transform of the following functions.
sin(
x), cos(x), sinh(x), cosh(x), x
n
, 'x, e
x
, heaviside(x), delta(x), delta(x, n)
ClassPad does not support transform of the following functions.
tan(
x), sin
– 1
(x), cos
– 1
(x), tan
– 1
(x), tanh(x), sinh
– 1
(x), cosh
– 1
(x), tanh
– 1
(x), log(x), ln(x), 1/x, abs(x), gamma(x)
Laplace Transform of a Differential Equation
The laplace command can be used to solve ordinary differential equations. ClassPad does not support System
of Differential Equations for laplace.
Syntax: laplace(diff eq,
x , y , t )
diff eq: differential equation to solve ; x : independent variable in the diff eq ;
y : dependent variable in the diff eq ; t : parameter of the transform
Example: To solve a differential equation
x ’ + 2 x = e
−
t
where x (0) = 3 using the
Laplace transform
Lp means F ( s ) = L [ f ( t )] in the result of transform for a differential equation.
u fourier [Action][Advanced][fourier], invFourier [Action][Advanced][invFourier]
Function: “fourier” is the command for the Fourier Transform, and “invFourier” is the command for the inverse
Fourier Transform.
Syntax: fourier( f ( x), x, w, n) invFourier( f ( w), w, x, n)
x : variable with respect to which the expression is transformed with ; w : parameter of the transform ;
n : 0 to 4, indicating Fourier parameter to use (optional)
ClassPad supports transform of the following functions.
sin(
t), cos(t), log(t), ln(t), abs(t), signum(t), heaviside(t), delta(t), delta(t,n), e
ti
ClassPad does not support transform of the following functions.
tan(t), sin
– 1
(t), cos
– 1
(t), tan
– 1
(t), sinh(t), cosh(t), tanh(t), sinh
– 1
(t), cosh
– 1
(t), tanh
– 1
(t), gamma(t), 't , e
t
The Fourier Transform pairs are defined using two arbitrary constants a, b.
∫
∞
–∞
()
ω

(ω) =
⏐
⏐
(2
π)
1–
∫
∞
–∞
(ω)
–ω
ω
() =
⏐
⏐
(2
π)
1+
The values of a and b depend on the scientific discipline, which can be specified by the value of n (optional
fourth parameter of fourier and invFourier) as shown below.