gusucode.com > symbolic工具箱matlab源码程序 > symbolic/@sym/laplace.m
function L = laplace(F,varargin) %LAPLACE Laplace transform. % L = LAPLACE(F) is the Laplace transform of the 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 z: L = L(z). % By definition, L(s) = int(F(t)*exp(-s*t),t,0,inf). % % L = LAPLACE(F,z) makes L a function of z instead of the default s: % LAPLACE(F,z) <=> L(z) = int(F(t)*exp(-z*t),t,0,inf). % % L = LAPLACE(F,w,u) makes L a function of u instead of the % default s (integration with respect to w). % LAPLACE(F,w,u) <=> L(u) = int(F(w)*exp(-u*w),w,0,inf). % % Examples: % syms a s t w x F(t) % laplace(t^5) returns 120/s^6 % laplace(exp(a*s)) returns -1/(a-z) % 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^(3/2),t) returns (3*pi^(1/2))/(4*t^(5/2)) % laplace(diff(F(t))) returns s*laplace(F(t),t,s) - F(0) % % See also SYM/ILAPLACE, SYM/FOURIER, SYM/ZTRANS, SUBS. % Copyright 2011 The MathWorks, Inc. L = transform('laplace', 't', 's', 'z', F, varargin{:}); end