Laplace Transform Calculator

Laplace Transform Calculator

Result:

Laplace Transform Theory

The Laplace Transform is defined as:

L{f(t)}=F(s)=โˆซ0โˆžeโˆ’stf(t)dt

Common Transforms

Time Domain (f(t)) Frequency Domain (F(s))
1 1s
eat 1sโˆ’a
tn n!sn+1
sinโก(ฯ‰t) ฯ‰s2+ฯ‰2

Properties

  • Linearity: L{af(t)+bg(t)}=aF(s)+bG(s)
  • Differentiation: L{fโ€ฒ(t)}=sF(s)โˆ’f(0)
  • Integration: L{โˆซ0tf(ฯ„)dฯ„}=F(s)s

Note: This calculator supports basic transforms. Complex functions may show integral form.

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