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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Milne Thompson Method for finding Analytic Function ： ウィキペディア英語版 Milne Thompson Method for finding Analytic Function Milne Thompson Method is a method of finding an Analytic Function, whose real or imaginary part is given. The method greatly simplifies the process of finding the Analytic Function, whose real or imaginary or any combination of the two parts is given. ==Method for finding the Analytic Function== Let $f(z)\; =\; u(x,y)\; +\; iv(x,y)$ be any Analytic Function. Let $z\; =\; x\; +\; iy$ and $\backslash bar\; \backslash \; =\; x\; -\; iy$ Hence, $x\; =\; \backslash frac\}\backslash$ Therefore, $f(z)\; =\; u(x,y)\; +\; iv(x,y)$ is equal to $f(z)\; =\; u(\; \backslash frac\}\backslash \; )\; +\; iv(\; \backslash frac\}\backslash \; )$ This can be regarded as an identity in two independent variables $z$ and $\backslash bar\; \backslash$. We can therefore, put $z$ = $\backslash bar\; \backslash$ and get $f(z)\; =\; u(z,0)\; +\; iv(z,0)$ So, $f(z)$ can be obtained in terms of $z$ simply by putting $x$ = $z$ and $y$ = $0$ in $f(z)\; =\; u(x,y)\; +\; iv(x,y)$ when $f(z)$ is Analytic Function. Now, $f\text{'}(z)\; =\; +\; i$. Since, $f(z)$ is Analytic, hence Cauchy-Riemann Equations are satisfied. Hence, $f\text{'}(z)\; =\; -\; i$. Let $$ = $\backslash Phi(x,y)$ and $$ = $\backslash Psi(x,y)$. Then, $f\text{'}(z)\; =\; -\; i$ $f\text{'}(z)\; =\; \backslash Phi(x,y)\; -\; i\backslash Psi(x,y)$ Now, putting $x\; =\; z$ and $y\; =\; 0$ in the above equation, we get $f\text{'}(z)\; =\; \backslash Phi(z,0)\; -\; i\backslash Psi(z,0)$. Integrating the above equation we get $\backslash int\; f\text{'}(z)\backslash ,dz\; =\; \backslash int\; \backslash Phi(z,0)\; dz\; -\; i\; \backslash int\; \backslash Psi(z,0)\; dz$ Or $f(z)\; =\; \backslash int\; f\text{'}(z)\backslash ,dz\; =\; \backslash int\; \backslash Phi(z,0)\; dz\; -\; i\; \backslash int\; \backslash Psi(z,0)\; dz\; +\; c$ which is the required Analytic Function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Milne Thompson Method for finding Analytic Function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.