The Laplace Transform of Derivatives and Integrals

In this video we take the Laplace Transform of derivatives or integrals. What's amazing is that these result in expressions entirely in terms of the original function. This will be important for us when we take the Laplace Transform of a differential equation because it will convert an ODE with initial conditions into an algebraic equation we can hopefully solve more easily.

Formulas:
1) L{f(t)}=sF(s)-f(0)
2)L{ integral from 0 to t of f(tau)} = F(s)/s

This is part of my series on the Laplace Transforms in my Differential Equations Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
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►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS

►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6

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► Want to learn math effectively? Check out my "Learning Math" Series:
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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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Видео The Laplace Transform of Derivatives and Integrals канала Dr. Trefor Bazett