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 $a=t_0<t_1<\cdots <t_k=b$ such that:

• $f^{\prime }$ exists on each interval $(t_i,t_{i+1})$
• $f^{\prime }$ is continuous on each interval $(t_i,t_{i+1})$
• $f$ and $f^{\prime }$ are bounded on each interval $(t_i,t_{i+1})$