# What's the difference between “boundary value problems” and “initial value problems”?

Mathematically speaking, is there any essential difference between initial value problems and boundary value problems?

The specification of the values of a function $f$ and the "velocities" $\frac{\partial f}{\partial t}$ at an initial time $t=0$ can also be seen, I think, as the specification of boundary values, since the boundaries of the variable $t$ are, usually, at $t=0$ and $t<\infty$.