Practice Convolution Theorem (13.1) - Convolution Theorem - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the definition of convolution?
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Look for the integral definition.
Question 2.
State one property of convolution.
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Think about the order of functions.
3Question 3.
What is the formula for convolution of two functions?
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Review the definition provided in this section.
4Question 4.
Is the Convolution theorem commutative?
- True
- False
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Think about as addition works.
Question 5.
Given $f(t) = e^{-3t}$ and $g(t) = t^2$ , find $(f * g)(t)$ .
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Consider using substitution for \$ t - \\tau \$.
Question 6.
Calculate the Laplace Transform of the convolution of two functions, where drivers are $f(t) = u(t)$ and $g(t) = u(t - 3)$ and verify the Convolution Theorem.
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Remember the properties of the Heaviside unit step function.

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