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Some corrections

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kongr45gpen committed Oct 2, 2017
1 parent 9f6b15f commit a8a2f70011f851f823d26481f5dee2f92075f6a0
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@@ -5567,10 +5567,7 @@ \subsection{Θεώρημα Cauchy}
\end{array} \)
\end{enumparen}
Τι σχέση έχουν όλα αυτά με \begin{enumparen}
\item Μιγαδικές συναρτήσεις;
\item Λογισμό II;
\end{enumparen}
Τι σχέση έχουν όλα αυτά με (1) μιγαδικές συναρτήσεις, (2) λογισμό II;
Τι ασκήσεις μπαίνουν στις εξετάσεις;
@@ -5624,11 +5621,11 @@ \subsection{Θεώρημα Cauchy}
-2u(m\delta,n\delta)-u\left(m\delta,(n-1)\delta\right)}{\delta^2}
\end{gather*}
\begin{gather*}
0 = u_{xx} + u_{yy} = \frac{
0 = u_{xx} + u_{yy} = \mathsmaller{\frac{
-4u(m\delta,n\delta) + u\left((m+1)\delta,n\delta\right)
+u\left(m\delta,(n+1)\delta\right)+u\left((m-1)\delta,n\delta\right)
+u\left(m\delta,(n-1)\delta\right)
}{\delta^2} \\
}{\delta^2}} \\
\implies u(m\delta,n\delta) = \frac{
u\left((m+1)\delta,n\delta\right)
+u\left((m-1)\delta,n\delta\right)
@@ -5762,7 +5759,7 @@ \subsection{Θεώρημα Cauchy}
\[
\left. \begin{array}{l}
u_1 = u(a) = ka+\lambda \\
u_1 = u(b) = kb+\lambda
u_2 = u(b) = kb+\lambda
\end{array} \right| \implies
\boxed{u(x,y) = \frac{u_1-u_2}{a-b}x + \underset{u_1}{?} }
\]
@@ -5796,7 +5793,7 @@ \subsection{Θεώρημα Cauchy}
\end{tikzpicture}
\begin{gather*}
\hat u(,\rho,\theta) = u(\theta) \\
\hat u(\rho,\theta) = u(\theta) \\
D = \left\lbrace (\rho,\theta): \theta_1 < \theta < \theta_2 \right\rbrace \\
D = \left\lbrace z: \theta_1 < \arg(z) < \theta_2 \right\rbrace \\
u(z) = u_1 \text{ όταν } \arg(z) = \theta_1 \\

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