Laplace transform - MATLAB laplace (2025)

Syntax Description Examples Laplace Transform of Symbolic Expression Specify Independent Variable and Transformation Variable Laplace Transforms of Dirac and Heaviside Functions Relation Between Laplace Transform of Function and Its Derivative Laplace Transform of Array Inputs Laplace Transform of Symbolic Function If Laplace Transform Cannot Be Found Input Arguments f — Input symbolic expression | symbolic function | symbolic vector | symbolic matrix var — Independent variable t (default) | symbolic variable transVar — Transformation variable s (default) | z | symbolic variable | symbolic expression | symbolic vector | symbolic matrix More About Laplace Transform Tips Algorithms Version History See Also Topics MATLAB Command Americas Europe Asia Pacific

syms x yf = 1/sqrt(x);F = laplace(f)

F =
$$\frac{\sqrt{\pi }}{\sqrt{s}}$$

syms a t yf = exp(-a*t);F = laplace(f)

F =
$$\frac{1}{a+s}$$

F = laplace(f,y)

F =
$$\frac{1}{a+y}$$

F = laplace(f,a,y)

F =
$$\frac{1}{t+y}$$

syms t ssyms a positiveF = laplace(dirac(t-a),t,s)

F =$${\mathrm{e}}^{-a\hspace{0.17em}s}$$

F = laplace(heaviside(t-a),t,s)

F =
$$\frac{{\mathrm{e}}^{-a\hspace{0.17em}s}}{s}$$

syms f(t) sDf = diff(f(t),t);F = laplace(Df,t,s)

F =$$s\hspace{0.17em}\mathrm{laplace}\left(f\left(t\right),t,s\right)-f\left(0\right)$$

syms a b c d w x y zM = [exp(x) 1; sin(y) 1i*z];vars = [w x; y z];transVars = [a b; c d];F = laplace(M,vars,transVars)

F =
$$\left(\begin{array}{cc}\frac{{\mathrm{e}}^x}{a}& \frac{1}{b}\\ \frac{1}{c^2+1}& \frac{\mathrm{i}}{d^2}\end{array}\right)$$

F = laplace(x,vars,transVars)

F =
$$\left(\begin{array}{cc}\frac{x}{a}& \frac{1}{b^2}\\ \frac{x}{c}& \frac{x}{d}\end{array}\right)$$

syms f1(x) f2(x) a bf1(x) = exp(x);f2(x) = x;F = laplace([f1 f2],x,[a b])

F =
$$\left(\begin{array}{cc}\frac{1}{a-1}& \frac{1}{b^2}\end{array}\right)$$

syms f(t) sf(t) = 1/t;F(s) = laplace(f,t,s)

F(s) =
$$\mathrm{laplace}\left(\frac{1}{t},t,s\right)$$

f(t) = ilaplace(F,s,t)

f(t) =
$$\frac{1}{t}$$

syms t;laplace(sin(t))

syms t;laplace(sin(t)*heaviside(t))