diff --git a/ana1.pdf b/ana1.pdf index 1d54767..1e9d845 100644 Binary files a/ana1.pdf and b/ana1.pdf differ diff --git a/ana1.tex b/ana1.tex index f5ce3ec..657f087 100644 --- a/ana1.tex +++ b/ana1.tex @@ -33,7 +33,7 @@ $0 < x \le 2$: $\forall n \ge \frac{2}{x}$, $f_n(x) = 0 = f(x)$ \item $f_n(x) = x^{n}$, $f_n\colon [0,1] \to \R$. \begin{figure}[ht!] - \begin{tikzpicture}[scale = 0.97] + \begin{tikzpicture}[scale = 0.95] \begin{axis}% [grid=both, minor tick num=4, @@ -50,7 +50,7 @@ \addplot[domain=0:1,samples=50,smooth,red] {x^4}; \end{axis} \end{tikzpicture} - \begin{tikzpicture}[scale = 0.97] + \begin{tikzpicture}[scale = 0.95] \begin{axis}% [grid=both, minor tick num=4, @@ -59,8 +59,7 @@ axis lines=middle, enlargelimits={abs=0.2}, ymax=1, - ymin=0, - xmax=1.1, + ymin=0 ] \addplot[domain=0:1.001,samples=1000,red] {(and(x>=0 , x<1) * 0 + (and(x>=1, x< 10) * 1}; \end{axis} @@ -97,7 +96,7 @@ \coloneqq \{ (x, y) \in D \times \R \mid | y - f(x)| < \epsilon\} .\] \begin{figure}[ht!] - \begin{tikzpicture}[scale = 0.97] + \begin{tikzpicture}[scale = 0.95] \begin{axis}% [grid=both, minor tick num=4, @@ -114,7 +113,7 @@ \addplot[domain=0:1,samples=50,smooth,dashed, blue] {0.3*sin(deg(8*x)) + 0.2*x + 0.3}; \end{axis} \end{tikzpicture} - \begin{tikzpicture}[scale = 0.97] + \begin{tikzpicture}[scale = 0.95] \begin{axis}% [grid=both, minor tick num=4, @@ -125,10 +124,10 @@ ymax=1, ymin=-0.4, ] - \addplot[domain=0:1.1,samples=50,smooth,dashed, blue] {0.3}; \addplot[domain=0:1.001,samples=1000,red] {(and(x>=0 , x<1) * 0 + (and(x>=1, x< 10) * 1}; \addplot[domain=0:1,samples=50,smooth,blue] {x^8}; - \addplot[domain=0:1.1,samples=50,smooth,dashed, blue] {-0.3}; + \addplot[domain=0:1,samples=50,smooth,dashed, blue] {0.3}; + \addplot[domain=0:1,samples=50,smooth,dashed, blue] {-0.3}; \end{axis} \end{tikzpicture} \caption{Links: ,,$\epsilon$-Schlauch``, Rechts: \ref{bsp:punktweisekonvergenz} (b) nicht gleichmäßig konvergent} diff --git a/ana22.tex b/ana22.tex index 8438227..05b933c 100644 --- a/ana22.tex +++ b/ana22.tex @@ -109,6 +109,35 @@ Die Integrabilitätsbedingungen sind nicht hinreichend. \end{enumerate} \end{definition} + +\begin{figure}[ht!] + \centering + \begin{tikzpicture} + \draw (0,0) -- node[left] {$s$} (0,2); + \draw (3,0) -- (3,2); + \draw[red] (0,0) -- node[below, black] {$t$} (3,0); + \draw[blue] (0,2) -- (3,2); + \draw[densely dashed] (0,0.67) -- (3,0.67); + \draw[densely dotted] (0,1.33) -- (3,1.33); + \node[below] at (0.1,0) {$a$}; + \node[below] at (2.9,0) {$b$}; + \node[left] at (0,0.15) {$0$}; + \node[left] at (0,1.85) {$1$}; + + \draw[->] (4,1) -- node[above] {$H$} (6,1); + + \draw[blue] (7,0) node[below left, black] {$A$} .. controls (8,2) .. node[sloped] {\tiny $\blacktriangleright$} (10,2) node[above right, black] {$B$}; + \draw[red] (7,0) .. controls (9,0) .. node[sloped] {\tiny $\blacktriangleright$} (10,2); + \draw[densely dashed] (7,0) .. controls (8.7,0.6) .. node[sloped] {\tiny $\blacktriangleright$} (10,2); + \draw[densely dotted] (7,0) .. controls (8.3,1.4) .. node[sloped] {\tiny $\blacktriangleright$} (10,2); + + \node[red ] at (9.5,0.5) {$\gamma_0$}; + \node[blue] at (7.5,1.5) {$\gamma_1$}; + \end{tikzpicture} + \caption{Stetige Deformation von $\gamma_0$ nach $\gamma_1$} +\end{figure} + + \begin{bsp} \label{bsp:ellipse-und-kreis} Ellipse: Seien $a, b > 0$. diff --git a/analysisII.pdf b/analysisII.pdf index 7f9523c..121072f 100644 Binary files a/analysisII.pdf and b/analysisII.pdf differ