Practice Properties Of Convolution (13.1.5) - Convolution Theorem - Mathematics - iii (Differential Calculus)

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define the term convolution in the context of Laplace Transforms.
Show hintHide hint
Think about how functions interact over time.
Question 2.
What property states that (𝑓 ∗ 𝑔)(𝑡) = (𝑔 ∗ 𝑓)(𝑡)?
Show hintHide hint
Reflect on the order of operations.
3Question 3.
What is the definition of convolution?
Show hintHide hint
Think about integrating products over an interval.
4Question 4.
True or False: The convolution of two functions is non-commutative.
- True
- False
Show hintHide hint
Recall the commutative property you learned earlier.
Question 5.
Find the convolution of two functions 𝑓(𝑡) = e^{-at} and 𝑔(𝑡) = e^{-bt}. Show all steps.
Show hintHide hint
Set up your integral and consider how each function behaves over time.
Question 6.
Explain and derive the inverse Laplace transform for 1/(s^2 + 1) using convolution.
Show hintHide hint
Look for pairs of known Laplace transforms that will yield the function when combined.

5 more questions in this section. Enroll free to practise them all.