\documentclass[usenames,dvipsnames]{article}
\usepackage{pgfplots}
Figura 1
codice prima figura
\begin{tikzpicture}
\begin{axis}[
scale=0.8,
axis x line=center,
axis y line=center,
xmin = -2,
xmax = 7.5,
ymin = -1,
ymax = 5,
xlabel = {$\vartheta$},
ylabel = {$\rho$},
xtick = \empty,
ytick = \empty,
axis equal image,
axis on top,
clip = false,
disabledatascaling
]
\addplot[ultra thick,Green,fill=Green!25] coordinates {(0,2) (6.28,2) (6.28,0) (0,0)};
\addplot[ultra thick,red] coordinates {(0,4) (6.28,4) (6.28,0)};
\addplot[very thick, dashed] coordinates {(0,2/3) (6.28,2/3)};
\addplot[very thick, dashed] coordinates {(0,4/3) (6.28,4/3)};
\addplot[very thick, dashed] coordinates {(2,0) (2,4)};
\addplot[very thick, dashed] coordinates {(4,0) (4,4)};
\addplot[ultra thick,OliveGreen,fill=OliveGreen!50] coordinates {(2,2/3) (4,2/3) (4,4/3) (2,4/3)} -- cycle;
\addplot[no marks] coordinates {(0,4)} node[left] {$R$};
\addplot[no marks] coordinates {(0,2/3)} node[left] {$\rho$};
\addplot[no marks] coordinates {(0,4/3)} node[left] {$\rho+\mathrm{d}\rho$};
\addplot[no marks] coordinates {(2,0)} node[below] {$\vartheta$};
\addplot[no marks] coordinates {(4,0)} node[below] {$\vartheta+\mathrm{d}\vartheta$};
\addplot[no marks] coordinates {(3,3)} node {\scalebox{1.5}{$D$}};
\draw[-stealth,ultra thick] (axis cs:7,4) to[bend right=-35] (axis cs:10,4);
\draw[stealth-,ultra thick] (axis cs:7,-1) to[bend right=+35] (axis cs:10,-1);
\addplot[no marks] coordinates {(8.5,5)} node {$\Phi$};
\addplot[no marks] coordinates {(8.5,-2)} node {$\Phi^{-1}$};
\end{axis}
\end{tikzpicture}
seconda figura
codice seconda figura
\begin{tikzpicture}
\begin{axis}[
scale=0.8,
axis x line=center,
axis y line=center,
xmin = 0,
xmax = 5,
ymin = 0,
ymax = 5,
xtick = \empty,
ytick = \empty,
axis equal image,
axis on top,
clip = false
]
\addplot[ultra thick, no marks] coordinates {(1.5,1) (3.5,1) (3.5,3) (1.5,3) (1.5,1)};
\addplot[ultra thick, no marks, dashed] coordinates {(0,1) (1.5,1) (1.5,0)};
\addplot[ultra thick, no marks, dashed] coordinates {(0,3) (2,3)};
\addplot[ultra thick, no marks, dashed] coordinates {(3.5,1) (3.5,0)};
\addplot[no marks] coordinates {(1,0)} node[below] {$u$};
\addplot[no marks] coordinates {(3.5,0)} node[below] {$u+h$};
\addplot[no marks] coordinates {(0,1)} node[left] {$v$};
\addplot[no marks] coordinates {(0,3)} node[left] {$v+k$};
\addplot[no marks] coordinates {(1.5,1)} node[above left] {$A_0$};
\addplot[no marks] coordinates {(1.5,3)} node[above left] {$D_0$};
\addplot[no marks] coordinates {(3.5,3)} node[above right] {$C_0$};
\addplot[no marks] coordinates {(3.5,1)} node[above right] {$B_0$};
\end{axis}
\end{tikzpicture}
terza figura
codice terza figura
\begin{tikzpicture}
\begin{axis}[
scale=0.8,
axis x line=center,
axis y line=center,
xmin = 0,
xmax = 5,
ymin = 0,
ymax = 5,
xtick = \empty,
ytick = \empty,
axis equal image,
axis on top,
clip = false
]
\addplot[-stealth,ultra thick] coordinates {(1,1.5) (2,3.5)};
\addplot[-stealth,ultra thick] coordinates {(1,1.5) (3.5,2)};
\addplot[ultra thick,dashed] coordinates {(2,3.5) (4.5,4)};
\addplot[ultra thick,dashed] coordinates {(3.5,2) (4.5,4)};
\addplot[ultra thick,dashed] coordinates {(0,1.5) (1,1.5) (1,0)};
\addplot[no marks] coordinates {(1,0)} node[below] {$x$};
\addplot[no marks] coordinates {(0,1.5)} node[left] {$y$};
\addplot[no marks] coordinates {(1,1.5)} node[below right] {$A_1$};
\addplot[no marks] coordinates {(1.5,2.5)} node[left] {$V_1$};
\addplot[no marks] coordinates {(2.5,1.75)} node[below] {$V_2$};
\end{axis}
\end{tikzpicture}
quarta figura
codice quarta figura
\begin{tikzpicture}
\begin{axis}[
scale=0.8,
axis x line=center,
axis y line=center,
xmin = -4,
xmax = 4,
ymin = -4,
ymax = 4,
xlabel = {$u$},
ylabel = {$v$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.5cm}O$},
xtick = \empty,
ytick = \empty,
axis equal image,
axis on top,
clip = false,
disabledatascaling
]
\addplot[ultra thick, smooth cycle, fill=blue!50] plot coordinates {(0,1) (2,1.5) (1.5, -2) (-1, -2) (-2.5, -1) (-2.5, 1.5)} node[above right] {$\Psi^{-1}(\Omega)$};
\addplot[ultra thick, smooth cycle] plot coordinates {(2.5,2.5) (3,-3.2) (-3.2,-2) (-3.1,3)} node[above left] {$D$};
\draw[-stealth,ultra thick] (axis cs:4,3) to[bend right=-35] (axis cs:8,3);
\addplot[draw=none] coordinates {(6,4.2)} node {$\Psi$};
\draw[stealth-,ultra thick] (axis cs:4,-3) to[bend right=35] (axis cs:8,-3);
\addplot[draw=none] coordinates {(6,-4.3)} node {$\Psi^{-1}$};
\end{axis}
\end{tikzpicture}
quinta figura
codice quinta figura
\begin{tikzpicture}
\begin{axis}[
scale=0.8,
axis x line=center,
axis y line=center,
xmin = -4,
xmax = 4,
ymin = -4,
ymax = 4,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.5cm}O$},
xtick = \empty,
ytick = \empty,
axis equal image,
axis on top
]
\addplot[ultra thick, smooth cycle, fill=blue!50] plot coordinates {(0,1.5) (1, 1) (1, -0.5) (0,-1.5) (-2, -2) (-2,0) (-1,1)} node[above left] {$\Omega$};
\addplot[ultra thick, smooth] plot coordinates {(-3,5) (0,3) (2,3) (2.5,0) (2,-2) (-2,-3) (-5,1)};
\addplot[draw=none] coordinates {(1,-3)} node[right] {$E = \Psi(D)$};
\end{axis}
\end{tikzpicture}