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The convolution of two functions, f and g supported on [0,+∞[, under the framework of the Laplace Transform can be writt
Posted: Wed Jul 13, 2022 5:05 am
by answerhappygod
- The Convolution Of Two Functions F And G Supported On 0 Under The Framework Of The Laplace Transform Can Be Writt 1 (32.15 KiB) Viewed 35 times
The convolution of two functions, f and g supported on [0,+∞[, under the framework of the Laplace Transform can be written as f∗g=∫−∞+∞f(t−τ)u(t−τ)g(τ)u(τ)dτ=∫0tf(t−τ)g(τ)dτ. The Convolution Theorem can be stated as L{f∗g}=F(s)G(s), 5 in which F(s)=L{f} and G(s)=L{g} are the Laplace Transform of f and g, respectively. Use the Convolution Theorem to determine the inverse Laplace Transform of (s2+k2)21, where k is a real constant.