It just means that the function is continuous, smooth and therefore differentiable (deriviatives, should you need to use them, will be valid).can you explain this sentence further
"The 0- inductor current is I0 and the application of a finite voltage can not change
the current in zero time, so iL0+=iL0-."
and why it cannot change "the current in zero time"
and why does it give us " iL0+=iL0-"