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Function: laplace (expr, t, s)
- The Laplace transform of expr with respect to the variable t and transform parameter s.
Example:
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Delta Function
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(%i)
laplace(delta(t), t, s);
(%o) 1
Unit Step Function
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(%i)
laplace(1, t, s);
(%o) 1/s
Trigonometric Function
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(%i)
laplace(sin(t), t, s);
(%o) 1/(s^2+1)
(%i) laplace(cos(t), t, s);
(%o) s/(s^2+1)
Exponential Function
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(%i) laplace(%e^(-a*t),t,s);
(%o) 1/(s+a)
(%i) laplace(%e^(-a*t)*t^2, t, s);
(%o) 2/(s+a)^3
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EXAMPLE: