I am examining functions and I would like to find where they have singularities. I know that the functions have singularities within the domain of interest, but it is not readily apparant from the function alone where they are. The domains of interest, however, are sufficiently large that I can't examine graphs of them.
If I can compute the integral around some complex domain that contains the (real) domain of interest, would it be possible to use complex analysis to determine the number of singularities?
If you have suggestions on how I can clarify this question, please let me know. I took complex analysis years ago and did poorly in it then. :(