Posts Tagged ‘convolution’

Why Doesn’t This Work?

December 19, 2007

A common example of integration by parts used in many Calculus II classes has students compute

$\int e^x \sin x\, dx$

by integrating by parts twice, then rearranging terms to arrive at a solution. This technique is handy for many functions whose derivatives eventually repeat, that is, functions satisfying

$f^{(n)}(x) = cf(x)$

for some integer n and some constant c. (Question: Is there a name for such functions? I feel like I should know this.) When does this technique fail?