let's suppose a function given in polar coordinate F(r,phi) and our purpose is to calculate the surface integral, say F(r,phi)dA over the region S defined by
S={ |Z|<b , |z-z0|>a } where Z=r*exp(1j*phi). it means the regions between the circles |Z|=b , |z-z0|=a . However, F(r,phi) has singularities inside the circle |z-z0|=a . therefore, we are not able to use integral(over circle |Z|<b )-integral(over circle |z-z0|<a) .
your help and consideration are much appreciated.
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