Wednesday, 19 June 2013

complex analysis - Definition of smooth curve


Definition of smooth curve: A parametric curve Z(t)=x(t)+i>y(t) on [a,b] is called smooth if




  1. Z(t)=x(t)+iy(t) exists and continuous on [a,b].


  2. Z(t) is non zero on (a,b).






But my problem is that why is the word "continuous" written? As We know that differentiability implies continuity.

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