Matlab 2009a
help laplace
--- help for sym/laplace ---
LAPLACE Laplace transform.
L = LAPLACE(F) is the Laplace transform of the scalar sym F with
default independent variable t. The default return is a function
of s. If F = F(s), then LAPLACE returns a function of t: L = L(t).
By definition L(s) = int(F(t)*exp(-s*t),0,inf), where integration
occurs with respect to t.
L = LAPLACE(F,t) makes L a function of t instead of the default s:
LAPLACE(F,t) <=> L(t) = int(F(x)*exp(-t*x),0,inf).
L = LAPLACE(F,w,z) makes L a function of z instead of the
default s (integration with respect to w).
LAPLACE(F,w,z) <=> L(z) = int(F(w)*exp(-z*w),0,inf).
Examples:
syms a s t w x
laplace(t^5) returns 120/s^6
laplace(exp(a*s)) returns 1/(t-a)
laplace(sin(w*x),t) returns w/(t^2+w^2)
laplace(cos(x*w),w,t) returns t/(t^2+x^2)
laplace(x^sym(3/2),t) returns 3/4*pi^(1/2)/t^(5/2)
laplace(diff(sym('F(t)'))) returns laplace(F(t),t,s)*s-F(0)
See also sym/ilaplace, sym/fourier, sym/ztrans.
Reference page in Help browser
doc sym/laplace
