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  • 12.1: Принцип аргументу
    https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%90%D0%BD%D0%B0%D0%BB%D1%96%D0%B7/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D1%96_%D0%B7%D0%BC%D1%96%D0%BD%D0%BD%D1%96_%D0%B7_%D0%B4%D0%BE%D0%B4%D0%B0%D1%82%D0%BA%D0%B0%D0%BC%D0%B8_(Orloff)/12%3A_%D0%9F%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF_%D0%B0%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D1%83/12.01%3A_%D0%9F%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF_%D0%B0%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D1%83
    \[\begin{array} {rclcl} {\int_{\gamma} \dfrac{(1 + f)' f(z)}{1 + f(z)} \ dz} & = & {\int_{\gamma} \dfrac{f' f(z)}{1 + f(z)} \ dz} & \ \ & {(\text{because } (1 + f)' = f')} \\ {\text{Ind} (1 + f \circ ...\[\begin{array} {rclcl} {\int_{\gamma} \dfrac{(1 + f)' f(z)}{1 + f(z)} \ dz} & = & {\int_{\gamma} \dfrac{f' f(z)}{1 + f(z)} \ dz} & \ \ & {(\text{because } (1 + f)' = f')} \\ {\text{Ind} (1 + f \circ \gamma, 0)} & = & {\text{Ind} (f \circ \gamma, -1)} & \ \ & {(1 + f \text{ winds around 0 } \Leftrightarrow \text{ winds around -1})} \\ {Z_{1 + f, \gamma}} & = & {Z_{1 + f, \gamma}} & \ \ & {(\text{same in both equation}))} \\ {P_{1 + f, \gamma}} & = & {P_{f, \gamma}} & \ \ & {(\text{poles of } f …
  • 3.8: Розширення та застосування теореми Гріна
    https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%90%D0%BD%D0%B0%D0%BB%D1%96%D0%B7/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D1%96_%D0%B7%D0%BC%D1%96%D0%BD%D0%BD%D1%96_%D0%B7_%D0%B4%D0%BE%D0%B4%D0%B0%D1%82%D0%BA%D0%B0%D0%BC%D0%B8_(Orloff)/03%3A_%D0%91%D0%B0%D0%B3%D0%B0%D1%82%D0%BE%D0%B2%D0%B0%D1%80%D1%96%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BE%D0%B1%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F_(%D0%BE%D0%B3%D0%BB%D1%8F%D0%B4)/3.08%3A_%D0%A0%D0%BE%D0%B7%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%BD%D1%8F_%D1%82%D0%B0_%D0%B7%D0%B0%D1%81%D1%82%D0%BE%D1%81%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B8_%D0%93%D1%80%D1%96%D0%BD%D0%B0
    ЯкщоD просто підключений іcurlF=0 включенийD, тоF=∇f для деякихf. ∮C1F⋅dr+∮C2F⋅dr=∫∫RcurlF dA. \[\oint_{C...ЯкщоD просто підключений іcurlF=0 включенийD, тоF=∇f для деякихf. ∮C1F⋅dr+∮C2F⋅dr=∫∫RcurlF dA. ∮C1F⋅dr+∮C2F⋅dr+∮C3F⋅dr+∮C4F⋅dr=∫∫RcurlF dA. ∫∫RcurlF dA=∫C1+C3+C2−C3F⋅dr=∫C1+C2F⋅dr.