- in the
complex plane that
satisfies ∮ γ f ( z ) d z = 0 {\displaystyle \
oint _{\gamma }f(z)\,dz=0} for
every closed piecewise C1
curve γ {\displaystyle...
- then ∮ C ( L d x + M d y ) = ∬ D ( ∂ M ∂ x − ∂ L ∂ y ) d A {\displaystyle \
oint _{C}(L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac...
- 0 , {\displaystyle -\
oint dS_{\text{Res}}=\
oint {\frac {\delta Q}{T_{\text{surr}}}}\leq 0,}
where ∮ d S Res {\displaystyle \
oint dS_{\text{Res}}} is the...
- 1 2 π i ∮ γ f ( z ) z − a d z . {\displaystyle f(a)={\frac {1}{2\pi i}}\
oint _{\gamma }{\frac {f(z)}{z-a}}\,dz.\,} The
proof of this
statement uses the...
- _{\Omega }} is a
volume integral over the
volume Ω, ∮ ∂ Σ {\displaystyle \
oint _{\partial \Sigma }} is a line
integral around the
boundary curve ∂Σ, with...
- ( v l × B ) ⋅ d l {\textstyle \
oint \left(\mathbf {v} \times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} =\
oint \left(\mathbf {v} _{l}\times \mathbf...
-
point z0 is
interior to γ, then ∮ γ d z z − z 0 = 2 π i . {\displaystyle \
oint _{\gamma }{\frac {dz}{z-z_{0}}}=2\pi i.}
Although the
curve γ is not a circle...
- _{\Sigma }(\nabla \times \mathbf {F} )\cdot \mathrm {d} \mathbf {\Sigma } =\
oint _{\partial \Sigma }\mathbf {F} \cdot \mathrm {d} \mathbf {\Gamma } .} More...
- {3}{4z}}}}\\&=-i\
oint _{C}{\frac {4}{3z^{3}+10z+{\frac {3}{z}}}}\,dz\\&=-4i\
oint _{C}{\frac {dz}{3z^{3}+10z+{\frac {3}{z}}}}\\&=-4i\
oint _{C}{\frac...
- {\begin{aligned}\
oint _{C}w'(z)\,dz&=\
oint _{C}(v_{x}-iv_{y})(dx+idy)\\&=\
oint _{C}(v_{x}\,dx+v_{y}\,dy)+i\
oint _{C}(v_{x}\,dy-v_{y}\,dx)\\&=\
oint _{C}\mathbf...
