contour integration residues eigen values dimension basis span linear independence zeros and poles series eigen vectors graphs of trigonometric functions quadrants derivatives sequences groups asymptotes basic concepts in calculus properties of rings complex analysis jordan's lemma upper semi circle type iii use of cauchy residue theorem residues and poles type ii polynomial function polynomial functions integrals over c evaluate integrals of typei ( trigonometric term ) poles diagonalizable algebraic multiplicity geometric multiplicity type iii integration type ii integration tests
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