[[곡선,curve]]
폐곡선 closed curve's orientation:
||positive  ||ccw ||
||negative  ||cw ||

단어
contour 윤곽, 등고선

path_integral이라고 안하네.

TBW: Compare: 단어만 보면 [[선적분,line_integral]]과 비슷한데 둘의 차이를 구분해서 서술. 같은거?

Def.
Let $f$ be defined at points of a smooth curve $C$ defined by
 $x=x(t),\,y=y(t),\;a\le t\le b.$
The '''contour integral''' of $f$ along $C$ is:
 $\int_C f(z)dz=\lim_{||P||\to0}\sum_{k=1}^{n} f(z_k^*) \Delta z_k$
(Zill AEM Def 18.1.1)

Thm. Evaluation of a Contour Integral
If $f$ is continuous on a smooth curve $C$ given by
 $z(t)=x(t)+iy(t),\;a\le t\le b,$
then:
 $\int_C f(z)dz=\int_a^b f(z(t))z'(t)dt$
(Zill AEM Thm 18.1.1)

= 성질 properties =
다음은 익숙
 * ∫,,C,, kf(z)dz= k∫,,C,, f(z)dz
 * ∫,,C,, (f(z) + g(z))dz = ∫,,C,, f(z)dz + ∫,,C,, g(z)dz
 * ∫,,C,, f(z)dz = ∫,,C₁,, f(z)dz + ∫,,C₂,, f(z)dz
 여기서 C는 매끄러운 곡선 C₁, C₂의 union
다음을 기억
 $\int_{-C}f(z)dz=-\int_C f(z)dz$ 여기서 -C는 반대 방향(orientation)을 의미(denote).

= thm =
[[코시-구르사_정리,Cauchy-Goursat_theorem]]
[[유수정리,residue_theorem]]

----
[[https://terms.naver.com/entry.naver?docId=5668872&ref=y&cid=60207&categoryId=60207 수학백과: 경로적분법]]
[[WpKo:경로적분법]]

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 [[적분,integration]]
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