Let be an interval and be a continuously differentiable function.

Solutions to the Schrödinger equation must be continuous, and continuously differentiable.

If these functions are r times continuously differentiable, f is called a C-diffeomorphism).

Note that "f" is not assumed to be continuously differentiable nor continuous on the closure of "G".

In physical applications the functions I and J are usually not only continuous but even continuously differentiable.

Let be a piecewise continuously differentiable function which is periodic with some period .

In particular, if a function is continuously differentiable then its Fourier series converges to it everywhere.

For mathematical reasons, it is usually assumed that is continuously differentiable.

The adjoining figure shows a continuously differentiable curve in blue.

Such processes are very common including, in particular, all continuously differentiable functions.