# 14.5: Shifting Theorem

This is a very useful theorem, and one that is almost trivial to prove. (Try it!) It is

14.5.1

For example, from the table, we have The shifting theorem tells us that

I'm sure you will now want to expand your table even more. Or you may want to go the other way, and cut down the table a bit! After all, you know that **L**(1) = 1/*s*. The shifting theorem, then, tells you that **L**(*e ^{at}*) = 1/(

*s*-

*a*), so that entry in the table is superfluous! Note that you can use the theorem to deduce either direct or inverse transforms.