Differential Equations › Section D · Laplace transforms › Topic D.7
Problems with step functions
This is where Laplace transforms leave the older methods behind. An input that switches on, off or changes formula partway through is handled in a single calculation, with the switching times carried along by exponential factors.
In this topic
- Where the transform pays off
- The strategy
- Worked example: a switch turned on
- Reading the answer
- The same problem without transforms
- Worked example: a pulse on a spring
- How smooth is the solution?
- Worked example: forcing that needs rewriting
- Common mistakes to avoid
- Key takeaways
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