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 .../kyotsu_2019_complex_function_theory.md    | 62 +++++++++++++++++++
 docs/kakomonn/kyushu_university/index.md      |  1 +
 mkdocs.yml                                    |  1 +
 3 files changed, 64 insertions(+)
 create mode 100644 docs/kakomonn/kyushu_university/ISEE/kyotsu_2019_complex_function_theory.md

diff --git a/docs/kakomonn/kyushu_university/ISEE/kyotsu_2019_complex_function_theory.md b/docs/kakomonn/kyushu_university/ISEE/kyotsu_2019_complex_function_theory.md
new file mode 100644
index 000000000..fe9c9b2fc
--- /dev/null
+++ b/docs/kakomonn/kyushu_university/ISEE/kyotsu_2019_complex_function_theory.md
@@ -0,0 +1,62 @@
+---
+comments: false
+title: 九州大学 システム情報科学府 情報理工学専攻・電気電子工学専攻 2019年度 複素関数論
+tags:
+  - Kyushu-University
+---
+# 九州大学 システム情報科学府 情報理工学専攻・電気電子工学専攻 2019年度 複素関数論
+
+
+## **Author**
+Zero
+
+## **Description**
+解析関数 $f(z) = u + iv$ を考える．ただし，$z = x + iy$ は複素数，$x$ と $y$ は実数，$u$ と $v$ は実数値関数，$i = \sqrt{-1}$ である．x と y が極形式 $x = r\cos\theta$ と $y = r\sin\theta$ で表されるとき，極形
+式のコーシー・リーマンの方程式は以下の式で書けることを示せ．
+
+$$
+\frac{\partial u}{\partial r} = \frac{1}{r}\frac{\partial v}{\partial \theta},\frac{\partial v}{\partial r} = -\frac{1}{r}\frac{\partial u}{\partial \theta}
+$$
+
+## **Kai** 
+コーシー・リーマンの方程式は以下の式表せる。
+
+$$
+\left \{
+\begin{align}
+&\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \tag{①} \\
+&\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} \tag{②} \\
+\end{align}
+\right.
+$$
+
+$$
+\begin{align}
+&\frac{\partial x}{\partial r} = \cos\theta ,\frac{\partial y}{\partial r} = \sin\theta \notag \\
+&\frac{\partial x}{\partial \theta} = -r\sin\theta, \notag \\
+&\frac{\partial y}{\partial \theta} = r\cos\theta \Leftrightarrow \cos\theta = \frac{1}{r}\frac{\partial y}{\partial \theta} \tag{③}
+\end{align}
+$$
+
+① の両辺に $\frac{\partial x}{\partial r} = \cos\theta$ をかける
+
+$$
+\begin{aligned}
+&\frac{\partial u}{\partial x} \cdot \frac{\partial x}{\partial r} = \frac{\partial v}{\partial y} \cdot \cos\theta \\
+&\frac{\partial u}{\partial r} = \frac{\partial v}{\partial y} \cdot \cos\theta \\
+&\frac{\partial u}{\partial r} = \frac{\partial v}{\partial y} \cdot \frac{1}{r}\frac{\partial v}{\partial \theta} \\
+\therefore &\frac{\partial u}{\partial r} = \frac{1}{r} \cdot \frac{\partial v}{\partial \theta}
+\end{aligned}
+$$
+
+② の両辺に $-\frac{\partial x}{\partial r} = -\cos\theta$ をかける
+
+$$
+\begin{aligned}
+&\frac{\partial u}{\partial y} \cdot (-\cos\theta) = \frac{\partial v}{\partial x} \cdot \frac{\partial x}{\partial r} \\
+&-\frac{\partial u}{\partial y} \cdot \cos\theta = \frac{\partial v}{\partial r} \\
+&\frac{\partial v}{\partial r} = -\frac{\partial u}{\partial y} \cdot \cos\theta \\
+&\frac{\partial v}{\partial r} = -\frac{\partial u}{\partial y} \cdot \frac{1}{r} \frac{\partial u}{\partial \theta} \\
+\therefore &\frac{\partial v}{\partial r} = -\frac{1}{r} \cdot \frac{\partial u}{\partial \theta} 
+\end{aligned}
+$$
diff --git a/docs/kakomonn/kyushu_university/index.md b/docs/kakomonn/kyushu_university/index.md
index 69074437a..96ef9184f 100644
--- a/docs/kakomonn/kyushu_university/index.md
+++ b/docs/kakomonn/kyushu_university/index.md
@@ -73,6 +73,7 @@ tags:
             - [解析学・微積分](ISEE/kyotsu_2019_analysis_calculus.md)
             - [ベクトル解析](ISEE/kyotsu_2019_vector_analysis.md)
             - [確率・統計](ISEE/kyotsu_2019_prob_stat.md)
+            - [複素関数論](ISEE/kyotsu_2019_complex_function_theory.md)
         - 2018年度:
             - [複素関数論](ISEE/kyotsu_2018_complex_function_theory.md)
         - 2016年度:
diff --git a/mkdocs.yml b/mkdocs.yml
index 009d512a6..ea4491347 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -924,6 +924,7 @@ nav:
             - 解析学・微積分: kakomonn/kyushu_university/ISEE/kyotsu_2019_analysis_calculus.md
             - ベクトル解析: kakomonn/kyushu_university/ISEE/kyotsu_2019_vector_analysis.md
             - 確率・統計: kakomonn/kyushu_university/ISEE/kyotsu_2019_prob_stat.md
+            - 複素関数論: kakomonn/kyushu_university/ISEE/kyotsu_2019_complex_function_theory.md
           - 2018年度:
             - 複素関数論: kakomonn/kyushu_university/ISEE/kyotsu_2018_complex_function_theory.md
           - 2016年度: