Laplace Transform Calculator
Common Laplace Transforms
Find the Laplace transform of standard functions
Inverse Laplace Transform
Find the inverse Laplace transform of common F(s) forms
Formula
L{f(t)} = ∫₀^∞ f(t)e^(-st)dt | L{eᵃᵗ} = 1/(s-a) | L{sin(ωt)} = ω/(s²+ω²)
Frequently Asked Questions
What is the Laplace transform?
The Laplace transform converts a function of time f(t) into a function of complex frequency F(s) = ∫₀^∞ f(t)e^(-st)dt. It is widely used to solve differential equations by converting them to algebraic equations in the s-domain.
When is the Laplace transform used?
It is commonly used in engineering for control systems, circuit analysis, signal processing, and solving linear ODEs with constant coefficients. It simplifies differential equations into algebraic ones that are easier to solve.
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