Contour integration of real functions

stefaneli
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I have a problem with choosing a contour for integration... Can someone explain to me when to use a keyhole contour and when a semi-circle? Thanks...:)
 
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stefaneli said:
I have a problem with choosing a contour for integration... Can someone explain to me when to use a keyhole contour and when a semi-circle? Thanks...:)

Use keyhole when you need to avoid singularities.
 
Singularities on real axis?
 
Yes. Like (sin x)/x.
 
Thanks man.:)
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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