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laplace
Laplace transform of a symbolic expression.
Category: Mathematics > Calculus
Syntax
F = laplace(f, t, s)Transforms f(t) into F(s) = int(f(t)*exp(-s*t), t, 0, Inf).
Description
The Laplace transform turns differential equations in t into algebraic equations in s. Derivatives become multiplication by s, and convolution becomes multiplication. For example the transform of t^2 is 2/s^3 and that of sin(t) is 1/(s^2 + 1). The result is brought back to time with ilaplace.
Input arguments
f- Symbolic expression in
t. t- Time variable.
s- Transform variable.
Output arguments
F- Symbolic expression in
s.
Example
Two transforms
syms t s
laplace(t^2, t, s)
laplace(sin(t), t, s)Output
ans = 2/s^3
ans = 1/(s^2 + 1)