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math:transforms [2025-11-14 Fri 03:42] – theorytoemath:transforms [2025-11-19 Wed 18:52] (current) – [Laplace Transforms] fix sign on e^at*cos(kt) transform theorytoe
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 | $$t\cos(kt)$$                  | $$\frac{s^2-k^2}{(s^2+k^2)^2}$$ | | $$t\cos(kt)$$                  | $$\frac{s^2-k^2}{(s^2+k^2)^2}$$ |
 | $$e^{at}\sin(kt)$$             | $$\frac{k}{(s-a)^2-k^2}$$       | | $$e^{at}\sin(kt)$$             | $$\frac{k}{(s-a)^2-k^2}$$       |
-| $$e^{at}\cos(kt)$$             | $$\frac{s-a}{(s-a)^2-k^2}$$     |+| $$e^{at}\cos(kt)$$             | $$\frac{s-a}{(s-a)^2+k^2}$$     |
 | $$\frac{\sin{at}}{t}$$         | $$\text{atan}\left(\frac{a}{s}\right)$$    | | $$\frac{\sin{at}}{t}$$         | $$\text{atan}\left(\frac{a}{s}\right)$$    |
 | $$\dot{f}(t)$$                 | $$sF(s) -f(0)$$                 | | $$\dot{f}(t)$$                 | $$sF(s) -f(0)$$                 |
math/transforms.1763091768.txt.gz · Last modified: by theorytoe

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