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 Apr14 accepted Improper Integral with trigonometric functions Apr14 comment Improper Integral with trigonometric functions Well this integral diverges so my integral will diverge by the comparison test. Correct? Apr14 asked Improper Integral with trigonometric functions Apr1 awarded Notable Question Mar17 comment Residue Theorem and Homologous to zero In your definition of being homologous to zero, if there is a point outside of $G$ that isn't so that the winding number is zero, then wouldn't that mean the the curve does not meet the hypothesis of the RT? Mar17 comment Residue Theorem and Homologous to zero This is the heart of my question I think. If $C_2$ is NOT homologous to 0, then it does not satisfy the hypothesis because in order to use the Residue Theorem, we need a curve that is homologous to 0. I apologize if I'm being stupid here... Mar17 comment Residue Theorem and Homologous to zero So this was my question; we don't consider such curves as $C_2$ for the residue theorem because it does not satisfy the hypothesis. Correct? Mar17 comment Residue Theorem and Homologous to zero Well in this picture the answer is no, you can't deform $C_2$ to a single point and still stay in $K$. Mar17 comment Residue Theorem and Homologous to zero So in this picture, $C_2$ is not homologous to 0? Then for the Residue Theorem we couldn't use a curve such as $C_2$ but can only consider curves that are either $C_1$ or curves that wrap around $H$ in such a way so that the winding number is 0, correct? Mar17 comment Residue Theorem and Homologous to zero I think I'm a little confused here. In this example $f=\frac{1}{z^2}$ and so is analytic on $\mathbb{C}-\{0\}$. Then if our contour is just the unit circle traversed once around this point, shouldn't the winding number be 1? Mar17 asked Residue Theorem and Homologous to zero Mar1 accepted Morera's Theorem and annuli Mar1 answered Morera's Theorem and annuli Mar1 asked Morera's Theorem and annuli Feb19 comment Consider the function I would try a sequential argument and use the denseness of $\mathbb{R}$. Feb19 comment A Step in the Proof of Green's Theorem Which limits are you talking about? Could you be more specific? Feb17 revised Did I do this proof right? Here is one proof. Feb12 awarded Teacher Feb12 answered Did I do this proof right? Feb1 awarded Critic