Improve readme

Makefile

@@ -3,8 +3,8 @@
 # Paths and filenames
 SRC_DIR  = src
 OUT_DIR  = out
-MAIN_TEX = $(SRC_DIR)/main.tex
+MAIN_TEX = main.tex   	# in SRC_DIR
-MAIN_PDF = $(OUT_DIR)/main.pdf
+MAIN_PDF = main.pdf  	# in OUT_DIR
 
 # LaTeX and Biber commands
 
@@ -19,14 +19,14 @@ default: english
 release: german english
 # Default target
 english: 
-	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(MAIN_TEX)
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(SRC_DIR)/$(MAIN_TEX)
 	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
-	mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_en_formula_collection.pdf
+	mv $(OUT_DIR)/$(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_en_Formulary.pdf
 
 german:
-	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[german]{babel}/' $(MAIN_TEX)
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[german]{babel}/' $(SRC_DIR)/$(MAIN_TEX)
 	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
-	mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_formelsammlung.pdf
+	mv $(OUT_DIR)/$(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_Formelsammlung.pdf
 
 # Clean auxiliary and output files
 clean:

readme.md

@@ -0,0 +1,111 @@
+# Formulary
+This is supposed to be a compact, searchable collection of the most important stuff I learned during my physics studides,
+because it would be a shame if I forget it all!
+
+## Building the PDF
+### Dependencies
+Any recent **TeX Live** distribution should work. You need:
+- `LuaLaTeX` compiler
+- several packages from ICAN
+- `latexmk` to build it
+
+### With GNU make
+1. In the project directory (where this `readme` is), run `make german` or `make english`.
+2. Rendered document will be `out/<date>_<formulary>.pdf`
+
+### With Latexmk
+1. Choose the language: In `main.tex`, set the language in `\usepackage[english]{babel}` to either `english` or `german`
+2. In the `src` directory, run `latexmk -lualatex main.tex`
+3. Rendered document will be `out/main.pdf`
+
+### With LuaLatex
+1. Choose the language: In `main.tex`, set the language in `\usepackage[english]{babel}` to either `english` or `german`
+2. Create the `.aux` directory
+3. In the `src` directory, run
+    - `lualatex  -output-directory="../.aux"  --interaction=nonstopmode --shell-escape "main.tex"` **3 times**
+4. Rendered document will be `.aux/main.pdf`
+
+# LaTeX Guideline
+Here is some info to help myself remember why I did things the way I did.
+
+In general, most content should be written with macros, so that the behaviour can be changed later.
+
+## Structure
+All translation keys and LaTeX labels should use a structured approach:
+`<key type>:<partname>:<section name>:<subsection name>:<...>:<name>`
+
+The `<partname>:...:<lowest section name>` will be defined as `\fqname` (fully qualified name) when using the `\Part`, `\Section`, ... commands.
+
+`<key type>` is:
+
+- formula: `f`
+- equation: `eq`
+- table: `tab`
+- figure: `fig`
+- parts, (sub)sections: `sec`
+
+### Files and directories
+Separate parts in different source files named `<partname>.tex`.  
+If a part should be split up in multiple source files itself, use a
+subdirectory named `<partname>` containing `<partname>.tex` and other source files for sections.  
+This way, the `fqname` of a section or formula partially matches the path of the source file it is in.
+
+## `formula` environment
+The main way to display something is the formula environment:
+```tex
+\begin{formula}{<key>}
+    \desc{English name}{English description}{$q$ is some variable, $s$ \qtyRef{some_quantity}}
+    \desc[german]{Deutscher Name}{Deutsche Beschreibung}{$q$ ist eine Variable, $s$ \qtyRef{some_quantity}}
+    <content>
+\end{formula}
+```
+Each formula automatically gets a `f:<section names...>:<key>` label.
+For the content, several macros are available:
+- `\eq{<equation>}` a wrapper for the `align` environment
+- `\fig[width]{<path>}`
+- `\quantity{<symbol>}{<units>}{<vector, scalar, extensive etc.>}` for physical quantites
+- `\constant{<symbol>}{ <values> }` for constants, where `<values>` may contain one or more `\val{value}{unit}` commands.
+
+### References
+**Use references where ever possible.**  
+In equations, reference or explain every variable. Several referencing commands are available for easy referencing:
+- `\fqSecRef{<fqname of section>}` prints the translated title of the section
+- `\fqEqRef{<fqname of formula>}` prints the translated title of the formula (first argument of `\desc`)
+- `\qtyRef{<key>}` prints the translated name of the quantity
+- `\QtyRef{<key>}` prints the symbol and the translated name of the quantity
+- `\constRef{<key>}` prints the translated name of the constant
+- `\ConstRef{<key>}` prints the symbol and the translated name of the constant
+- `\elRef{<symbol>}` prints the symbol of the chemical element
+- `\ElRef{<symbol>}` prints the name of the chemical element
+
+
+## Multilanguage
+All text should be defined as a translation (`translations` package, see `util/translation.tex`).
+Use `\dt` or `\DT` or the the shorthand language commands `\eng`, `\Eng` etc. to define translations.
+These commands also be write the translations to an auxiliary file, which is read after the document begins.
+This means (on subsequent compilations) that the translation can be resolved before they are defined.  
+Use the `gt` or `GT` macros to retrieve translations.
+The english translation of any key must be defined, because it will also be used as fallback.
+
+Lower case macros are relative to the current `fqname`, while upper case macros are absolute.
+
+Never make a macro that would have to be changed if a new language was added, eg dont do
+```tex
+% 1: key, 2: english version, 3: german version
+\newcommand{\mycmd}[3]{
+    \dosomestuff{english}{#1}{#2}
+    \dosomestuff{german}{#1}{#3}
+}
+
+\mycmd{key}{this is english}{das ist deutsch}
+```
+Instead, do
+```tex
+% [1]: lang, 2: key, 2: text
+\newcommand{\mycmd}[3][english]{
+    \dosomestuff{#1}{#2}{#3}
+}
+
+\mycmd{key}{this is english}
+\mycmd[german]{key}{das ist deutsch}
+```

src/ed/ed.tex

@@ -6,134 +6,3 @@
 % pure electronic stuff in el
 % pure magnetic stuff in mag
 % electromagnetic stuff in em
-
-% TODO move
-\Section[
-    \eng{Hall-Effect}
-    \ger{Hall-Effekt}
-    ]{hall}
-
-    \begin{formula}{cyclotron}
-        \desc{Cyclontron frequency}{}{}
-        \desc[german]{Zyklotronfrequenz}{}{}
-        \eq{\omega_\text{c} = \frac{e B}{\masse}}
-    \end{formula}
-    \TODO{Move}
-
-
-    \Subsection[
-        \eng{Classical Hall-Effect}
-        \ger{Klassischer Hall-Effekt}
-        ]{classic}
-        \begin{ttext}
-            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
-            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
-        \end{ttext}
-        \begin{formula}{voltage}
-            \desc{Hall voltage}{}{$n$ charge carrier density}
-            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
-            \eq{U_\text{H} = \frac{I B}{ne d}}
-        \end{formula}
-
-        \begin{formula}{coefficient}
-            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
-            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
-            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{}
-            \desc[german]{Spezifischer Widerstand}{}{}
-            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
-        \end{formula}
-
-
-    \Subsection[
-        \eng{Integer quantum hall effect}
-        \ger{Ganzahliger Quantenhalleffekt}
-    ]{quantum}  
-
-        \begin{formula}{conductivity}
-            \desc{Conductivity tensor}{}{}
-            \desc[german]{Leitfähigkeitstensor}{}{}
-            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-        \end{formula}
-
-        \begin{formula}{resistivity_tensor}
-            \desc{Resistivity tensor}{}{}
-            \desc[german]{Spezifischer Widerstands-tensor}{}{}
-            \eq{
-                \rho = \sigma^{-1}
-                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-            }
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
-            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
-            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
-        \end{formula}
-
-        % \begin{formula}{qhe}
-        %     \desc{Integer quantum hall effect}{}{}
-        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
-        %     \fig{img/qhe-klitzing.jpeg}
-        % \end{formula}
-
-        \begin{formula}{fqhe}
-            \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
-            \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
-            \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
-        \end{formula}
-
-        \begin{ttext}
-            \eng{
-                \begin{itemize}
-                    \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
-                    \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
-                    \item \textbf{Spin} (QSHE): spin currents instead of charge currents
-                    \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
-                \end{itemize}
-            }
-            \ger{
-                \begin{itemize}
-                    \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
-                    \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
-                    \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
-                    \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
-                \end{itemize}
-            }
-        \end{ttext}
-    
-
-    \TODO{sort}
-    \begin{formula}{impedance_c}
-        \desc{Impedance of a capacitor}{}{}
-        \desc[german]{Impedanz eines Kondesnators}{}{}
-        \eq{Z_{C} = \frac{1}{i\omega C}}
-    \end{formula}
-
-    \begin{formula}{impedance_l}
-        \desc{Impedance of an inductor}{}{}
-        \desc[german]{Impedanz eines Induktors}{}{}
-        \eq{Z_{L} = i\omega L}
-    \end{formula}
-
-    \TODO{impedance addition for parallel / linear}
-
-\Section[
-    \eng{Dipole-stuff}
-    \ger{Dipol-zeug}
-]{dipole}
-
-    \begin{formula}{poynting}
-        \desc{Dipole radiation Poynting vector}{}{}
-        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
-        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
-    \end{formula}
-
-    \begin{formula}{power}
-        \desc{Time-average power}{}{}
-        \desc[german]{Zeitlich mittlere Leistung}{}{}
-        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
-    \end{formula}

src/ed/misc.tex

@@ -0,0 +1,131 @@
+% TODO move
+\Section[
+    \eng{Hall-Effect}
+    \ger{Hall-Effekt}
+    ]{hall}
+
+    \begin{formula}{cyclotron}
+        \desc{Cyclontron frequency}{}{}
+        \desc[german]{Zyklotronfrequenz}{}{}
+        \eq{\omega_\text{c} = \frac{e B}{\masse}}
+    \end{formula}
+    \TODO{Move}
+
+
+    \Subsection[
+        \eng{Classical Hall-Effect}
+        \ger{Klassischer Hall-Effekt}
+        ]{classic}
+        \begin{ttext}
+            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
+            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
+        \end{ttext}
+        \begin{formula}{voltage}
+            \desc{Hall voltage}{}{$n$ charge carrier density}
+            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
+            \eq{U_\text{H} = \frac{I B}{ne d}}
+        \end{formula}
+
+        \begin{formula}{coefficient}
+            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
+            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
+            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{}
+            \desc[german]{Spezifischer Widerstand}{}{}
+            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
+        \end{formula}
+
+
+    \Subsection[
+        \eng{Integer quantum hall effect}
+        \ger{Ganzahliger Quantenhalleffekt}
+    ]{quantum}  
+
+        \begin{formula}{conductivity}
+            \desc{Conductivity tensor}{}{}
+            \desc[german]{Leitfähigkeitstensor}{}{}
+            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+        \end{formula}
+
+        \begin{formula}{resistivity_tensor}
+            \desc{Resistivity tensor}{}{}
+            \desc[german]{Spezifischer Widerstands-tensor}{}{}
+            \eq{
+                \rho = \sigma^{-1}
+                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+            }
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
+            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
+            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
+        \end{formula}
+
+        % \begin{formula}{qhe}
+        %     \desc{Integer quantum hall effect}{}{}
+        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
+        %     \fig{img/qhe-klitzing.jpeg}
+        % \end{formula}
+
+        \begin{formula}{fqhe}
+            \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
+            \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
+            \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
+        \end{formula}
+
+        \begin{ttext}
+            \eng{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
+                    \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
+                    \item \textbf{Spin} (QSHE): spin currents instead of charge currents
+                    \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
+                    \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
+                    \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
+                    \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
+                \end{itemize}
+            }
+        \end{ttext}
+    
+
+    \TODO{sort}
+    \begin{formula}{impedance_c}
+        \desc{Impedance of a capacitor}{}{}
+        \desc[german]{Impedanz eines Kondesnators}{}{}
+        \eq{Z_{C} = \frac{1}{i\omega C}}
+    \end{formula}
+
+    \begin{formula}{impedance_l}
+        \desc{Impedance of an inductor}{}{}
+        \desc[german]{Impedanz eines Induktors}{}{}
+        \eq{Z_{L} = i\omega L}
+    \end{formula}
+
+    \TODO{impedance addition for parallel / linear}
+
+\Section[
+    \eng{Dipole-stuff}
+    \ger{Dipol-zeug}
+]{dipole}
+
+    \begin{formula}{poynting}
+        \desc{Dipole radiation Poynting vector}{}{}
+        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
+        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
+    \end{formula}
+
+    \begin{formula}{power}
+        \desc{Time-average power}{}{}
+        \desc[german]{Zeitlich mittlere Leistung}{}{}
+        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
+    \end{formula}
+

src/main.tex

@@ -1,7 +1,7 @@
 %! TeX program = lualatex
 % (for vimtex)
 \documentclass[11pt, a4paper]{article}
-% \usepackage[utf8]{inputenc}
+% SET LANGUAGE HERE
 \usepackage[english]{babel}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 % ENVIRONMENTS etc
@@ -277,6 +277,7 @@
 \Input{ed/el}
 \Input{ed/mag}
 \Input{ed/em}
+\Input{ed/misc}
 
 \Input{quantum_mechanics}
 \Input{atom}
@@ -287,7 +288,7 @@
 \Input{cm/charge_transport}
 \Input{cm/low_temp}
 \Input{cm/semiconductors}
-\Input{cm/other}
+\Input{cm/misc}
 \Input{cm/techniques}
 
 \Input{topo}

src/math/calculus.tex

@@ -11,7 +11,71 @@
     %     }
     % \end{formula}
 
+        
     \Subsection[
+        \eng{Fourier analysis}
+        \ger{Fourieranalyse}
+    ]{fourier}
+        \Subsubsection[
+            \eng{Fourier series}
+            \ger{Fourierreihe}
+        ]{series}
+            \begin{formula}{series}
+                \desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
+                \desc[german]{Fourierreihe}{Komplexe Darstellung}{}
+                \eq{f(t) = \sum_{k=-\infty}^{\infty} c_k \Exp{\frac{2\pi \I kt}{T}}}
+            \end{formula}
+            \Eng[real]{real}
+            \Ger[real]{reellwertig}
+            \begin{formula}{coefficient-complex}
+                \desc{Fourier coefficients}{Complex representation}{}
+                \desc[german]{Fourierkoeffizienten}{Komplexe Darstellung}{}
+                \eq{
+                    c_k &= \frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Exp{-\frac{2\pi \I}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
+                    c_{-k} &= \overline{c_k} \quad \text{\GT{if} $f$ \GT{real}}
+                }
+            \end{formula}
+
+            \begin{formula}{series_sincos}
+                \desc{Fourier series}{Sine and cosine representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
+                \desc[german]{Fourierreihe}{Sinus und Kosinus Darstellung}{}
+                \eq{f(t) = \frac{a_0}{2} + \sum_{k=1}^{\infty} \left(a_k \Cos{\frac{2\pi}{T}kt} + b_k\Sin{\frac{2\pi}{T}kt}\right)}
+            \end{formula}
+            \begin{formula}{coefficient}
+                \desc{Fourier coefficients}{Sine and cosine representation\\If $f$ has point symmetry: $a_{k>0}=0$, if $f$ has axial symmetry: $b_k=0$}{}
+                \desc[german]{Fourierkoeffizienten}{Sinus und Kosinus Darstellung\\Wenn $f$ punktsymmetrisch: $a_{k>0}=0$, wenn $f$ achsensymmetrisch: $b_k=0$}{}
+                \eq{
+                    a_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Cos{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
+                    b_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Sin{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge1\\
+                    a_k &= c_k + c_{-k}      \quad\text{\GT{for}}\,k\ge0\\
+                    b_k &= \I(c_k - c_{-k})  \quad\text{\GT{for}}\,k\ge1
+                }
+            \end{formula}
+        \TODO{cleanup}
+        
+
+        \Subsubsection[
+            \eng{Fourier transformation}
+            \ger{Fouriertransformation}
+        ]{trafo}
+            \begin{formula}{transform}
+                \desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
+                \desc[german]{Fouriertransformierte}{}{}
+                \eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
+            \end{formula}
+
+            \Eng[linear_in]{linear in}
+            \Ger[linear_in]{linear in}
+            \GT{for} $f\in L^1(\R^n)$:
+            \begin{enumerate}[i)]
+                \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
+                \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
+                \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
+                \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
+            \end{enumerate}
+
+
+        \Subsubsection[
             \eng{Convolution}
             \ger{Faltung / Konvolution}
         ]{conv}
@@ -56,69 +120,6 @@
                 \eq{(f*g)^* = f^* * g^*}
             \end{formula}
 
-    \Subsection[
-        \eng{Fourier analysis}
-        \ger{Fourieranalyse}
-    ]{fourier}
-        \Subsubsection[
-            \eng{Fourier series}
-            \ger{Fourierreihe}
-        ]{series}
-            \begin{formula}{series}
-                \desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
-                \desc[german]{Fourierreihe}{Komplexe Darstellung}{}
-                \eq{f(t) = \sum_{k=-\infty}^{\infty} c_k \Exp{\frac{2\pi \I kt}{T}}}
-            \end{formula}
-            \Eng[real]{real}
-            \Ger[real]{reellwertig}
-            \begin{formula}{coefficient-complex}
-                \desc{Fourier coefficients}{Complex representation}{}
-                \desc[german]{Fourierkoeffizienten}{Komplexe Darstellung}{}
-                \eq{
-                    c_k &= \frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Exp{-\frac{2\pi \I}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
-                    c_{-k} &= \overline{c_k} \quad \text{\GT{if} $f$ \GT{real}}
-                }
-            \end{formula}
-
-            \begin{formula}{series_sincos}
-                \desc{Fourier series}{Sine and cosine representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
-                \desc[german]{Fourierreihe}{Sinus und Kosinus Darstellung}{}
-                \eq{f(t) = \frac{a_0}{2} + \sum_{k=1}^{\infty} \left(a_k \Cos{\frac{2\pi}{T}kt} + b_k\Sin{\frac{2\pi}{T}kt}\right)}
-            \end{formula}
-            \begin{formula}{coefficient}
-                \desc{Fourier coefficients}{Sine and cosine representation\\If $f$ has point symmetry: $a_{k>0}=0$, if $f$ has axial symmetry: $b_k=0$}{}
-                \desc[german]{Fourierkoeffizienten}{Sinus und Kosinus Darstellung\\Wenn $f$ punktsymmetrisch: $a_{k>0}=0$, wenn $f$ achsensymmetrisch: $b_k=0$}{}
-                \eq{
-                    a_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Cos{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
-                    b_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Sin{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge1\\
-                    a_k &= c_k + c_{-k}      \quad\text{\GT{for}}\,k\ge0\\
-                    b_k &= \I(c_k - c_{-k})  \quad\text{\GT{for}}\,k\ge1
-                }
-            \end{formula}
-        \TODO{cleanup}
-        
-
-
-        \Subsubsection[
-            \eng{Fourier transformation}
-            \ger{Fouriertransformation}
-        ]{trafo}
-            \begin{formula}{transform}
-                \desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
-                \desc[german]{Fouriertransformierte}{}{}
-                \eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
-            \end{formula}
-
-            \Eng[linear_in]{linear in}
-            \Ger[linear_in]{linear in}
-            \GT{for} $f\in L^1(\R^n)$:
-            \begin{enumerate}[i)]
-                \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
-                \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
-                \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
-                \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
-            \end{enumerate}
-
 
     \Subsection[
         \eng{Misc}
@@ -147,6 +148,12 @@
             \eq{\delta(f(x)) = \frac{\delta(x-x_0)}{\abs{g'(x_0)}}}
         \end{formula}
 
+        \begin{formula}{geometric_series}
+            \desc{Geometric series}{}{$\abs{q}<1$}
+            \desc[german]{Geometrische Reihe}{}{}
+            \eq{\sum_{k=0}^{\infty}q^k = \frac{1}{1-q}}
+        \end{formula}
+
 
     \Subsection[
         \eng{Logarithm}

src/readme.md

@@ -1,58 +0,0 @@
-# Knowledge Collection
-This is supposed to be a compact, searchable collection of the most important stuff I had to during my physics studides,
-because it would be a shame if I forget it all!
-
-# LaTeX Guideline
-Here is some info to help myself remember why I did things the way I did.
-
-In general, most content should be written with macros, so that the behaviour can be changed later.
-
-## `fqname`
-All translation keys and LaTeX labels should use a structured approach:
-`<key type>:<partname>:<section name>:<subsection name>:<...>:<name>`
-
-The `<partname>:...:<lowest section name>` will be defined as `fqname` (fully qualified name) macro when using the `\Part`, `\Section`, ... macros.
-
-`<key type>` should be
-
-- equation: `eq`
-- table: `tab`
-- figure: `fig`
-- parts, (sub)sections: `sec`
-
-### Reference functions
-Functions that create a hyperlink (and use the translation of the target element as link name):
-- `\fqSecRef{}`
-- `\fqEqRef{}`
-
-
-## Multilanguage
-All text should be defined as a translation (`translations` package, see `util/translation.tex`).
-Use `\dt` or `\DT` or the the shorthand language commands `\eng`, `\Eng` etc. to define translations.
-These commands also be write the translations to an auxiliary file, which is read after the document begins.
-This means (on subsequent compilations) that the translation can be resolved before they are defined.  
-Use the `gt` or `GT` macros to retrieve translations.
-The english translation of any key must be defined, because it will also be used as fallback.
-
-Lower case macros are relative to the current `fqname`, while upper case macros are absolute.
-
-Never make a macro that would have to be changed if a new language was added, eg dont do
-```tex
-% 1: key, 2: english version, 3: german version
-\newcommand{\mycmd}[3]{
-    \dosomestuff{english}{#1}{#2}
-    \dosomestuff{german}{#1}{#3}
-}
-
-\mycmd{key}{this is english}{das ist deutsch}
-```
-Instead, do
-```tex
-% [1]: lang, 2: key, 2: text
-\newcommand{\mycmd}[3][english]{
-    \dosomestuff{#1}{#2}{#3}
-}
-
-\mycmd{key}{this is english}
-\mycmd[german]{key}{das ist deutsch}
-```