# PWC1

Learned in MATH213 for Fourier Series.

Definition 4: Piecewise C1

A function $f$ is Piecewise $C_{1}$ (PWC1) on the interval $[a,b]$ if there is a finite partition $a=t_{0}<t_{1}<⋯<t_{k}=b$ such that:

- $f_{′}$ exists on each interval $(t_{i},t_{i+1})$
- $f_{′}$ is continuous on each interval $(t_{i},t_{i+1})$
- $f$ and $f_{′}$ are bounded on each interval $(t_{i},t_{i+1})$