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Interpreting the Laplace

by dijkarte
Tags: interpreting, laplace
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Mar15-12, 06:02 PM
P: 200
Thought it's pretty related to this forum. I'm familiar with applications of both Laplace and Fourier in physics and differential equations. However I still struggling trying to figure out the intuitive interpretation of both transforms or at least a mathematical illustration that shows their nature. We apply Laplace to a function but what do we get relative to the function? All the texts I have been reading state formulas and with a minimal proof/deduction if any. And the only interpretation they have is it transforms from one domain to another. Any good detailed reading that explains why and what exactly these transforms do?

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Mar20-12, 05:31 PM
P: 200
As I'm doing some reading about the derivation of Fourier series in complex form, how the following sums up??? Sorry that I lack the common sense of an average math student, but I insist to learn :)

sum(1, inf){ c[n]*exp(inwt) + c[-n]*exp(-inwt) } = sum(-inf, inf){ c[n]*exp(inwt) } ??????

No single book shows the derivation.
Mar20-12, 09:56 PM
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