• 공학수학2_복소해석 . . . . 36 matches
       Contour integral
       // [[경로적분,contour_integral]]
        $\bullet\;$ contour or path → piecewise-smooth [[곡선,curve|curve]]
        $\bullet\; \int_C f(z)dz$ → integral of $f(z)$ on contour $C$
        $\bullet\; \oint_C f(z)dz$ → integral of $f(z)$ on closed contour $C$
        $\bullet\; \int_C f(z)dz$ → also referred to as contour or complex integral
       Properties of contour integrals
       ● Sometimes we just want to figure out the bounding values of a contour integral
       every simple closed contour $C$ lying entirely in domain $D$ can be shrunk to a point without leaving $D$
       for every simple closed contour $C$ in $D$
       ● If $f$ is analytic at all points within and on a simple closed contour $C,$ then
       But $z=0$ is not a point interior to or on contour $C$
       Deformation of contours
       ● evaluate integral over a funky simple closed contour by replacing with a convenient contour.
       ● Contour $C$ is too funky, let's deform it.
       Equation of contour $C_1$
       (C,,k,,는 different contours)
       - these two points lie within contour $C$
       - we will replace contour $C$ with contours $C_1$ and $C_2$
       $=0:$ because $C_1,C_2$ does not contain the point $z=-i,$ hence the function $\frac{1}{z+i}$ is analytic on and within the contour
• 경로적분,contour_integral . . . . 8 matches
       [[복소평면,complex_plane]]에서의 [[선적분,line_integral]].[* [[WpEn:Contour_integration]] 맨 위 "This article is about the line integral in the complex plane."]
       [[경로,contour]] 위에서 [[복소함수,complex_function]]의 적분.[* 수학백과 첫줄]
       The '''contour integral''' of $f$ along $C$ is:
       Thm. Evaluation of a Contour Integral
       [[WpEn:Path_integral]]은 line integral, contour integral과의 혼동을 우려해 disambiguation page로 처리.
       https://planetmath.org/contourintegral
       https://mathworld.wolfram.com/ContourIntegral.html
       [[경로,contour]]
• 코시-구르사_정리,Cauchy-Goursat_theorem . . . . 6 matches
       for every simple closed contour $C$ in $D$
       ● If $f$ is analytic at all points within and on a simple closed contour $C,$ then
       Suppose that a function $f$ is analytic in a simply connected domain $D$ and that $f'$ is continuous in $D.$ Then for every simple closed contour $C$ in $D:$
       Suppose a function $f$ is analytic in a simply connected domain $D.$ Then for every simple closed contour $C$ in $D:$
       If $f$ is analytic at all points within and on a simple closed contour $C,$ then
       [[경로적분,contour_integral]]
• 곡선,curve . . . . 5 matches
       [[경로적분,contour_integral]]에서 언급되는데 TBW. [[선적분,line_integral]]과도 관련있는듯
       contour
        윤곽, 윤곽선(contour line), (syn. 외형, 가장자리).
        contour integral = [[경로적분,contour_integral]].
• 기울기,gradient . . . . 5 matches
       등고선/등위선/contour 와 직교한다. CHK
       gradient는 [[http://tomoyo.ivyro.net/123/wiki.php/asdf?action=fullsearch&value=contour&context=20&case=1|contour]] plot/map/curve, [[http://tomoyo.ivyro.net/123/wiki.php/asdf?action=fullsearch&value=%EB%93%B1%EA%B3%A0%EC%84%A0&context=20&case=1|등고선]] 과 관련있는데 TBW.
        벡터가 등고선에 수직. perpendicular to the contour line.
        또, gradient도 always perpendicular to the contour line.
• 닫힌경로,closed_path . . . . 5 matches
       closed_contour ... 닫힌 [[경로,contour]]
       https://proofwiki.org/wiki/Definition:Contour#Closed_Contour
       https://proofwiki.org/wiki/Definition:Contour/Closed
• 적분,integration . . . . 4 matches
        [[경로적분,contour_integral]]
       으로 번역되는 단어는 contour/path integral이 있음.
        * contour integral - 유수 정리 (residue theorem)와 관련
        Go to [[경로적분,contour_integral]]
• 복소해석,complex_analysis . . . . 2 matches
       [[경로적분,contour_integral]]
        [[경로,path]] [[경로,contour]] [[독립성,independence]]
• MIT_Multivariable_Calculus . . . . 1 match
       contour_plot 얘기
• 기울기벡터,gradient_vector . . . . 1 match
       $z=f(x,y)$ 에 대한 contour plot이 있는 상황.
• 길이,length . . . . 1 match
       [[경로,contour]]
• 방향도함수,directional_derivative . . . . 1 match
       level curve 등위선, 등위곡선, 등고선(등고선은 대개 contour line으로 번역)
• 선적분,line_integral . . . . 1 match
       단어만 보면 [[경로적분,contour_integral]]과 비슷한데 차이 구분하여 서술. Compare. TBW.
• 스토크스_정리,Stokes_theorem . . . . 1 match
       '''Stokes's theorem''' converts the [[면적분,surface_integral]] of the [[회전,curl]] of a vector over an open surface S into a [[선적분,line_integral]] of the vector along the contour C bounding the surface S.
• 운동,motion . . . . 1 match
       [[경로,contour]]
• 회전,curl . . . . 1 match
       벡터장 $\vec{B}$ 에서 $\nabla\times\vec{B}=0$ 이면, 그 벡터장은 conservative or irrotational하다고 한다. Because its circulation([[회전,curl]] 참조), represented by the RHS of (Stokes' Thm), is zero, irrespective of the contour chosen.

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