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I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases.
Thank you.
Thank you.
Which cases are those? I'm afraid you'll have to be a little more specific.I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases.
Thank you.
I'm afraid your link was 404'ed, i.e. not found.Thank you.
For example, in the RLC circuit from this page below, how could you know that Laplace transform and its inverse transform exist before using them?
In that example, I see that the author used Laplace and inverse transforms without considering the conditions for these transforms to exist.
http://people.seas.harvard.edu/~jones/es154/lectures/lecture_0/Laplace/laplace.html [Broken]
Yes, I read that and did many exercises about Laplace transform to consider about the existence of it.The Laplace transform is defined by an integral. The transform exists if the integral converges (i.e. its value is finite).
I hope so!The integral does converge for a large class of functions (including the solutions of any linear differential equation with constant coefficients) so in practice the question of existence isn't very important.