Practice Applications (1.2) - Laplace Transform of Derivatives - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is L{f'(t)}?
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Recall the formula and how it converts derivatives.
Question 2.
Define what an Initial Value Problem is.
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Focus on the 'initial' part.
3Question 3.
What is the first formula for the Laplace Transform of the first derivative?
- L{f'(t)} = sF(s) - f(0)
- L{f'(t)} = s²F(s) - sf(0) - f'(0)
- L{f(t)} = F(s)
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Look for the formula related to the first derivative.
4Question 4.
True or False: The Laplace Transform converts time-domain functions into frequency-domain functions.
- True
- False
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Think about the purpose of the Laplace Transform.
Question 5.
Demonstrate how you would transform the equation y' + y = e^(-t) into an algebraic equation using Laplace Transform.
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Remember to include y(0) when applying the transform to y'.
Question 6.
Given initial conditions y(0) = 3 and y'(0) = 0, find the solution of the differential equation y'' + 4y = 0.
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Focus on the solution process for Y(s) first.

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