I'm currently studying complex analysis, and I've found two differnent definitions of a smooth path. Here's one defined as in Beck's book:
A path $\gamma$ is smooth if it's continuously differentiable and has nonzero derivatives.
However, some authors define a smooth path without requiring $\gamma$ to have nonzero derivatives. I'm just wondering why would I need the condition of having nonzero derivatives, since being continuously differentiable already ensures the existence of the contour integral. Could anyone give some examples to illustrate the point? Thanks.