Practice Summary (1.3) - Laplace Transform of Derivatives - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the Laplace Transform of the first derivative?
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Remember the general transformation rule.
Question 2.
What transformation does L{f(t)} yield?
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Think about the integral of the function.
3Question 3.
What is L{f'(t)}?
- L{f'(t)} = sF(s) - f(0)
- L{f'(t)} = s²F(s) - f(0)
- L{f'(t)} = F(s) - tf(0)
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Think about the basic formula for the Laplace transformation.
4Question 4.
True or False: The Laplace Transform can only be applied to first derivatives.
- True
- False
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Review the formulas for different orders of derivatives.
Question 5.
Derive the Laplace Transform of f'(t) using integration by parts from first principles.
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Pay close attention to the boundary terms as t approaches infinity.
Question 6.
Prove that L{f' + g' (t)} = L{f(t)} + L{g(t)} for two functions and their derivatives.
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Consider how the Laplace Transform can be distributed across addition.

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