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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