added vector addition and scaling example

cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex

@@ -66,6 +66,11 @@ e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\
 \end{align*}
 
 \section{Ableitungen}
+
+\begin{align*}
+    (\log x)' &= \frac{1}{x}
+\end{align*}
+
 \begin{table}[ht]
 \begin{minipage}[b]{0.5\linewidth}\centering
 \begin{align*}

tikz/vector-addition-and-scaling/Makefile

@@ -0,0 +1,31 @@
+SOURCE = vector-addition-and-scaling
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/vector-addition-and-scaling/vector-addition-and-scaling.tex

@@ -0,0 +1,34 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{shapes, calc, shapes, arrows} 
+\usepackage{amsmath,amssymb}
+
+\usepackage{xcolor}
+\definecolor{xvectorcolor}{HTML}{77933C}
+
+\begin{document}
+\begin{tikzpicture}[font=\boldmath]\large
+    % Punkte
+    \coordinate (A) at (0,0) {};
+    \coordinate (B) at (2,0) {};
+    \coordinate (C) at (1,1) {};
+    \coordinate (D) at (3,1) {};
+
+    % Draw the triangle
+    \draw[thick, blue!25]  (B) -- (D) node[sloped,midway,above] {};
+    \draw[thick, red!25]   (C) -- (D) node[sloped,midway,above] {};
+    \draw[->, ultra thick, red,   arrows={-latex}]  (A) -- (B) node[sloped,right=-0.3cm, above] {$\mathsf{w}$};
+    \draw[->, ultra thick, blue,  arrows={-latex}]  (A) -- (C) node[sloped,midway,above=-0.1cm] {$\mathsf{v}$};
+    \draw[->, ultra thick, black, arrows={-latex}]  (A) -- (D) node[sloped,midway,above=-0.1cm] {$\mathsf{v+w}$};
+
+
+    \begin{scope}[shift={(0,1.5)}]
+    \draw[thick, blue!25]  (4,0) -- (5,1) node[sloped,midway,above] {};
+    \draw[thick, red!25]   (1,1) -- (5,1) node[sloped,midway,above] {};
+    \draw[->, ultra thick, red!25,   arrows={-latex}]  (0,0) -- (2,0);
+    \draw[->, ultra thick, red,   arrows={-latex}]  (0,0) -- (4,0) node[sloped,right=-0.7cm,above] {$\mathsf{2 \cdot w}$};
+    \draw[->, ultra thick, blue,  arrows={-latex}]  (0,0) -- (1,1) node[sloped,midway,above=-0.1cm] {$\mathsf{v}$};
+    \draw[->, ultra thick, black, arrows={-latex}]  (0,0) -- (5,1) node[sloped,midway,above=-0.1cm] {$\mathsf{v+2 \cdot w}$};
+    \end{scope}
+\end{tikzpicture}
+\end{document}