Laplace Transform: Second Shifting Theorem

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Laplace Transform: First Shifting Theorem
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Laplace Transform: Second Shifting Theorem
Here we calculate the Laplace transform of a particular function via the “second shifting theorem”. This video may be thought of as a basic example. The second shifting theorem is a useful tool when faced with the challenge of taking the Laplace transform of the product of a shifted unit step function (Heaviside function) with another shifted function. The Laplace transform is very useful in solving ordinary differential equations. Such an example is seen in 2nd year mathematics courses at university.

Second shifting theorem of Laplace transforms
This video shows how to apply the second shifting theorem of Laplace transforms. Several examples are presented to illustrate how to use the concepts. Such ideas are seen in university mathematics.

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Laplace Transform of tf(t)
The video presents a simple proof of an result involving the Laplace transform of tf(t). In particular it is shown that the Laplace transform of tf(t) is -F'(s), where F(s) is the Laplace transform of f(t). The proof involves an application of Leibniz rule for differentiating integrals. I also give an example at the end illustrating how to apply the proven result. Laplace transforms find important applications in solving ordinary differential equations with discontinuities. Such ideas are seen in 2nd-year university mathematics courses.

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