13.1.5.2 - Associative
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Practice Questions
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What is the definition of convolution?
💡 Hint: Think about how two functions are combined in the integral.
State one property of convolution.
💡 Hint: Recall the properties that allow rearranging or regrouping functions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Convolution Theorem state?
💡 Hint: Think about how transformations relate in the Laplace domain.
True or False: Convolution is always commutative.
💡 Hint: Recall properties discussed earlier in class.
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Challenge Problems
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Given $f(t) = e^{-t}$ and $g(t) = u(t)$, derive $(f * g)(t)$ using the definition of convolution.
💡 Hint: Substituting u(t-\\tau) might simplify your calculation.
Prove that convolution is commutative, meaning show $(f * g)(t) = (g * f)(t)$.
💡 Hint: Start from the definitions and apply the properties of the integral.
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