Differential Equations › Section D · Laplace transforms › Topic D.1
The definition of the Laplace transform
The Laplace transform turns a function of time into a function of a new variable, and in doing so turns differential equations into algebra. Everything in this section rests on one improper integral, so it pays to understand it properly.
In this topic
- Why transform at all?
- Piecewise continuous functions
- The definition
- Improper integrals: a quick review
- Worked example: exponentials and constants
- Worked example: the transform of t
- Worked example: a switched-off signal
- A harder integral: cosine
- When does the transform exist?
- Common mistakes to avoid
- Key takeaways
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