Syntax:

 

laplace( f(t), t, s)

invLaplace(L(s), s, t)

f(t): expression ;

L(s): expression ;

t: variable with respect to which the expression is

s: variable with respect to which the expression is

transformed ;

transformed ;

s: parameter of the transform

t: parameter of the transform

ClassPad supports transform of the following functions.

sin(x), cos(x), sinh(x), cosh(x), xn, 'x, ex, 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’ + 2x = 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.

ufourier [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), eti

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 , et

The Fourier Transform pairs are defined using two arbitrary constants a, b.

 

⏐⏐

∞

 

⏐⏐

∞

(ω) =

 

∫– ∞ ()ω

() =

 

∫– ∞ (ω)–ωω

(2π)1–

(2π)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.

Chapter 2: Main Application

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