Differential Equations › Section D · Laplace transforms › Topic D.8
The Dirac delta function
A hammer blow, a lightning strike on a power line, a sudden dose of medicine: some inputs are huge but last almost no time. The Dirac delta function models them as perfect instantaneous impulses, and its Laplace transform is the simplest of all.
In this topic
- Sudden blows
- A tall, thin pulse
- The defining properties
- Worked example: sifting
- The transform of the delta
- Steps and deltas
- Worked example: a struck spring
- Why the velocity jumps
- Worked example: a damped system struck once
- Impulse response
- Common mistakes to avoid
- Key takeaways
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