Practice Convolution Theorem (18.1.1) - Application to Integral Equations

Practice: Convolution Theorem

Lesson 18.1.1Application to Integral Equations

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6 sample questions

Question 1.
What is an integral equation?
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Think about the form of equations you see that include an integral.
Question 2.
What is the kernel in a Volterra Integral Equation?
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Consider how functions interact in the integral.
3Question 3.
What does the Convolution Theorem state?
- It states that convolution can be ignored in computation.
- It relates the convolution of functions to their Laplace Transforms.
- It is only applicable in discrete mathematics.
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Think about how we can simplify problems in calculus.
4Question 4.
True or False: The Laplace Transform converts integrals directly into sums.
- True
- False
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Consider the nature of transforms versus sums.
Question 5.
Solve the integral equation f(t) = 3 + ∫_{0}^{t} (t − τ)f(τ)dτ where f(0) = 1.
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Consider initial conditions when applying Laplace.
Question 6.
Derive f(t) if f(t) = 2 + ∫_{0}^{t} cos(t − τ)f(τ)dτ.
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Start by applying the Laplace Transform and resetting the cos function using transformations.

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