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What is the difference between sigular point for a function and the one in a vector field? Is the derivative or divergence at the singular point must be infinity? By the way, what is the relation between divergence and winding number? Any help or suggestion will be appreciated!

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How much complex analysis do you know? This is standard material in any complex analysis textbook. –  Potato Aug 25 '13 at 6:31
    
@Potato Could you give the formula than just comment? The concepts of winding number and residue confuse me. –  Eden Harder Aug 25 '13 at 7:06
    
Well, they're big concepts, and it's hard to explain them because I don't know your background. Have you looked at the Wikipedia article on the Residue theorem? That might be a good starting point. –  Potato Aug 25 '13 at 7:12

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