Question

This operation yields a value proportional to the negative-first coefficient of a Laurent series in a theorem named for that coefficient. Édouard Goursat ("gore-SAH") showed that a form of this operation vanishes for a holomorphic function over a simply connected domain (0[1])while improving upon (20[1])a proof by Cauchy (20[1]0[1])("KOH-shee"). The residue theorem (20[1])is used (20[1]0[1])to (20[1])perform (20[1])this (20[1])operation, (20[2]0[1])which is applied in both two and three (*) dimensions (10[1])in Stokes's (10[1]0[1])theorem. (10[5]0[3])A "fundamental (0[1])theorem" (10[1])reduces (10[2])this operation (10[1])to a difference (10[1]0[1])between two values of the (10[1])function (10[2]0[1])capital-F. (10[1])A "curtain" visualizes (10[1])the "line" form of this operation (10[1])that can be calculated (10[1])"by (10[1])parts" or with u-substitution. (10[3])For 10 (10[1])points, (10[1])name this operation that yields (10[1])a function's antiderivative. (10[2])■END■ (10[4]0[1])

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