Practice Associative - 13.1.5.2 | 13. Convolution Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Associative

13.1.5.2 - Associative

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Practice Questions

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Question 1 Easy

What is the definition of convolution?

💡 Hint: Think about how two functions are combined in the integral.

Question 2 Easy

State one property of convolution.

💡 Hint: Recall the properties that allow rearranging or regrouping functions.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Convolution Theorem state?

The product of two functions is always zero.
The inverse Laplace transform of the product of two functions is their convolution.
Convolution operates on discrete functions only.

💡 Hint: Think about how transformations relate in the Laplace domain.

Question 2

True or False: Convolution is always commutative.

True
False

💡 Hint: Recall properties discussed earlier in class.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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