The Final and Initial Value Theorems

Lecture slides: final-and-initial-value-theorems.pdf Download final-and-initial-value-theorems.pdf

The final value theorem can be used to find the limit of a function as t tends to infinity from properties of it's Laplace transform. Here we introduce and discuss these ideas.

The initial value theorem can be used to find the value of a function when t equals zero. Apparently this has something to do with turning bikes.

See Wikipedia for more info on the proof (to expand on this a bit, for any given A, the given bounds show that limit is within epsilon of f(0) - epsilon can then be made arbitrarily small by making A large enough).

More on bikes:

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