18.1.1 - Convolution Theorem
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Practice Questions
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What is an integral equation?
💡 Hint: Think about the form of equations you see that include an integral.
What is the kernel in a Volterra Integral Equation?
💡 Hint: Consider how functions interact in the integral.
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Interactive Quizzes
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What does the Convolution Theorem state?
💡 Hint: Think about how we can simplify problems in calculus.
True or False: The Laplace Transform converts integrals directly into sums.
💡 Hint: Consider the nature of transforms versus sums.
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Challenge Problems
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Solve the integral equation f(t) = 3 + ∫_{0}^{t} (t − τ)f(τ)dτ where f(0) = 1.
💡 Hint: Consider initial conditions when applying Laplace.
Derive f(t) if f(t) = 2 + ∫_{0}^{t} cos(t − τ)f(τ)dτ.
💡 Hint: Start by applying the Laplace Transform and resetting the cos function using transformations.
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