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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the convolution of f(t) = t and g(t) = e^{-t}?
💡 Hint: Use integration by parts to solve the integral.
Question 2
Easy
How do we use the Laplace transform in solving differential equations?
💡 Hint: Identify the initial conditions before applying the transform.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the result of the convolution of f(t) = t and g(t) = e^{-t}?
- (t-1) + e^{-t}
- (t+1)e^{-t}
- t^2 + e^{-t}
💡 Hint: Think of the integral representation of convolution.
Question 2
True or False: Convolution allows us to convert a differential equation into an algebraic equation.
- True
- False
💡 Hint: Consider the conversion process.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Evaluate the convolution of f(t) = sin(t) and g(t) = cos(t). Provide detailed steps showing the setup and final result.
💡 Hint: Use angles for simplifying the integration.
Question 2
Solve the differential equation y'' + 2y' + y = e^{-t} using convolution and provide the solution expression.
💡 Hint: Express the right side with the impulse response for simplification.
Challenge and get performance evaluation