Calculus with Complex NumbersCRC Press, 13 mar 2003 - 112 This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theo |
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Application calculus Cauchy's theorem circle centre closed contour complex numbers complex variables Consider the integral constant continuous contour integral converges Corollary cos2 cosh cosz coth cotz define defined derivative differentiable dx dy equation evaluate example exists f dz f f(z)dz fact Figure Find first follows formula function fundamental theorem geometric given gives graph half Hence imaginary indicated Inequality inside y integrand Laurent expansion length logz Maclaurin expansion method number of zeros Observe obtain origin parametrise plane points polynomial powers primitive principal value Proof properties Prove putting radius represents residue theorem rigorous round rule side Similarly simple pole singularities sinh sinz substitution Suppose tanz Taylor expansion term unit circle valid w-plane write zeros inside