Differential Equations › Section D · Laplace transforms › Topic D.9
Convolution integrals
The transform of a product is not the product of the transforms. But there is an operation in t whose transform is a product: convolution. It inverts awkward transforms, and it solves equations whose forcing is not even known yet.
In this topic
- Products of transforms
- The convolution integral
- Properties of convolution
- The convolution theorem
- Worked example: two routes to one answer
- Dividing by s means integrating
- Worked example: an unknown input
- Response as weighted memory
- Integral equations
- Common mistakes to avoid
- Key takeaways
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