19.21. (a) Show that f(z) dz can be written as A · dr + i B. dr, where A = (u, -v,0), B = (v, u, 0), and dr : (b) Show that both A and B have vanishing curls when f is analytic. (c) Now use the...

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19.21. (a) Show that f(z) dz can be written as<br>A · dr + i<br>B. dr,<br>where A = (u, -v,0), B = (v, u, 0), and dr :<br>(b) Show that both A and B have vanishing curls when f is analytic.<br>(c) Now use the Stokes' theorem to prove the Cauchy-Goursat theorem.<br>(dx, dy, 0).<br>

Extracted text: 19.21. (a) Show that f(z) dz can be written as A · dr + i B. dr, where A = (u, -v,0), B = (v, u, 0), and dr : (b) Show that both A and B have vanishing curls when f is analytic. (c) Now use the Stokes' theorem to prove the Cauchy-Goursat theorem. (dx, dy, 0).

Jun 04, 2022

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19.21. (a) Show that f(z) dz can be written as A · dr + i B. dr, where A = (u, -v,0), B = (v, u, 0), and dr : (b) Show that both A and B have vanishing curls when f is analytic. (c) Now use the...

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