Practice Laplace Transform Of The First Derivative (1.1.3)

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Exercise
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6 sample questions

Question 1.
What is the Laplace Transform of the function f(t) = t?
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Use the formula for the Laplace Transform.
Question 2.
Write down the formula for the Laplace Transform of the first derivative.
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Remember the connection between `F(s)` and `f(0)`.
3Question 3.
What is the Laplace Transform of the first derivative?
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Recall the derived formula from class.
4Question 4.
Laplace Transform converts which type of equations into algebraic ones?
- True
- False
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Think about how we convert differential terms into algebraic ones.
Question 5.
Derive the Laplace Transform of f(t) = e^{at} and show how to apply it to a differential equation.
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Start from basic properties of the Laplace Transform.
Question 6.
Given y' + 2y = e^{3t} with y(0) = 1, use Laplace Transform to find y(t).
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Remember to apply the Laplace of the forcing term correctly.

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