- ( 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...
- C ( L d x + M d y ) = ∬ D ( ∂ M ∂ x − ∂ L ∂ y ) d x d y {\displaystyle \
oint _{C}(L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac...
- ( ψ ) d γ {\displaystyle \
oint _{\partial \Sigma }{\mathbf {F} (\mathbf {x} )\cdot \,\mathrm {d} \mathbf {\Gamma } }=\
oint _{\gamma }{\mathbf {F} ({\boldsymbol...
- {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...
- 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...
- x + u d y ) {\displaystyle \
oint _{\gamma }f(z)\,dz=\
oint _{\gamma }(u+iv)(dx+i\,dy)=\
oint _{\gamma }(u\,dx-v\,dy)+i\
oint _{\gamma }(v\,dx+u\,dy)} By...
- 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...
-
structure only. The right-hand side is
sometimes written as ∮∂Ωω{\textstyle \
oint _{\partial \Omega }\omega } to
stress the fact that the (n−1){\displaystyle...
-
poles on C, then 12πi∮Cf′(z)f(z)dz=Z−P{\displaystyle {\frac {1}{2\pi i}}\
oint _{C}{f'(z) \over f(z)}\,dz=Z-P}
where Z and P
denote respectively the number...
- {\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...
