Analysis Chapter 1

Analysis Chapter 1 and Neorged everything for Analysis

.gitignore

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+*.norg

README.md

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-# ITET-Notes
-
-Hier findest du meine Notizen zu den Fächern vom Studiengang ITET.
-
-Andere Dateien wie Lösungen zu Serien findest du auf meiner [ETH Website](https://eth.jirayuruh.ch).
-
-Die LaTeX Template ist inspiriert durch den Template von [Senior Mars](https://github.com/SeniorMars/dotfiles/tree/main/latex_template).
-
-## DISCLAIMER!!!
-
-Ich übernehme keine Haftung über mögliche Fehler in den Notizen und Zusammenfassungen (Es hat sicherlich ein paar drinnen, da ich teils Sätze umformuliert habe und meine Persönliche Notizen beigefügt habe!).
-
-Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden. Sie sind in der Fehlerliste ersichtlich.
-
----
-
-Made by JirR02 in Switzerland 🇨🇭

README.org

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+#+title: ITET Notes
+
+#+author: JirR02
+Hier findest du meine Notizen zu den Fächern vom Studiengang ITET.
+
+Andere Dateien wie Lösungen zu Serien findest du auf meiner
+[[https://eth.jirayuruh.ch][ETH Website]].
+
+Die LaTeX Template ist inspiriert durch den Template von
+[[https://github.com/SeniorMars/dotfiles/tree/main/latex_template][Senior
+Mars]].
+
+* DISCLAIMER!!!
+:PROPERTIES:
+:CUSTOM_ID: disclaimer
+:END:
+Ich übernehme keine Haftung über mögliche Fehler in den Notizen und
+Zusammenfassungen (Es hat sicherlich ein paar drinnen, da ich teils
+Sätze umformuliert habe und meine Persönliche Notizen beigefügt habe!).
+
+Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden.
+Sie sind in der Fehlerliste ersichtlich.
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭

fs25/README.md

@@ -1,22 +0,0 @@
-# ITET 2. Semester (FS 2025)
-
-Im zweiten Semester habe ich die folgenden Fächer belegt:
-
-- [Analysis I und II](https://eth.jirayuruh.ch/fs25/analysis/)
-- [Grundzüge des Rechts](https://eth.jirayuruh.ch/fs25/grundzuege-recht/)
-- [Informatik I](https://eth.jirayuruh.ch/fs25/informatik/)
-- [Mathematische Methoden](https://eth.jirayuruh.ch/fs25/math_methoden/)
-- [Netzwerke und Schaltungen II](https://eth.jirayuruh.ch/fs25/nus/)
-- [Physik I](https://eth.jirayuruh.ch/fs25/physik/)
-
-Weitere Information findet ihr im VZZ oder auf eurer Moodle Seite.
-
-## DISCLAIMER!!!
-
-Ich übernehme keine Haftung über mögliche Fehler in den Notizen (Es hat sicherlich ein paar drinnen, da ich teils Sätze umformuliert habe und meine Persönliche Notizen beigefügt habe!).
-
-Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden. Sie sind in der Fehlerliste ersichtlich.
-
----
-
-Made by JirR02 in Switzerland 🇨🇭

fs25/README.org

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+#+title: ITET 2. Semester (FS 2025)
+
+#+author: JirR02
+Im zweiten Semester habe ich die folgenden Fächer belegt:
+
+- [[https://eth.jirayuruh.ch/fs25/analysis/][Analysis I und II]]
+- [[https://eth.jirayuruh.ch/fs25/grundzuege-recht/][Grundzüge des
+  Rechts]]
+- [[https://eth.jirayuruh.ch/fs25/informatik/][Informatik I]]
+- [[https://eth.jirayuruh.ch/fs25/math_methoden/][Mathematische
+  Methoden]]
+- [[https://eth.jirayuruh.ch/fs25/nus/][Netzwerke und Schaltungen II]]
+- [[https://eth.jirayuruh.ch/fs25/physik/][Physik I]]
+
+Weitere Information findet ihr im VZZ oder auf eurer Moodle Seite.
+
+* DISCLAIMER!!!
+:PROPERTIES:
+:CUSTOM_ID: disclaimer
+:END:
+Ich übernehme keine Haftung über mögliche Fehler in den Notizen (Es hat
+sicherlich ein paar drinnen, da ich teils Sätze umformuliert habe und
+meine Persönliche Notizen beigefügt habe!).
+
+Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden.
+Sie sind in der Fehlerliste ersichtlich.
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭

fs25/analysis_I_II/graphs/main.py

@@ -0,0 +1,15 @@
+from manim import *
+
+
+class ball(Scene):
+    def construct(self):
+
+        self.camera.background_color = WHITE
+
+        circ1 = Circle(radius=1, color=PURPLE, fill_opacity=1).move_arc_center_to(
+            3 * LEFT
+        )
+        circ2 = Circle(radius=1, color=BLUE, fill_opacity=0.5)
+        circ3 = Circle(radius=1, color=GREEN).move_arc_center_to(3 * RIGHT)
+
+        self.add(circ1, circ2, circ3)

fs25/analysis_I_II/grundlagen/funktionen.tex

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+\section{Funktionen}
+
+Intuitiv ist eine Funktion (oder Abbildung) von $X$ nach $Y$ eine Vorschrift, die jedem Element $x \in X$ ein eindeutiges Element $y \in Y$ zuordnet. \cite{Ziltner2024}
+
+\dfn{Funktion}{
+	Eine Funktion (oder Abbildung) ist ein Tripel
+
+	\[
+		f = (X, Y, G)
+		,\]
+
+	wobei $X$ und $Y$ Mengen sind und $G \subseteq X \times Y$ eine Teilmenge, sodass es für jedes $x \in X$ genau ein $y \in Y$ gibt, sodass $(x,y) \in G$.
+
+	\cite{Ziltner2024}
+}
+
+\dfn{Definitionsbereich, Zielbereich, Graph, Wert in einem Punkt}{
+	Für die Funktion $f$ haben wir folgende Definitonen um die Eigenschaften einer Funktion zu definieren.
+
+	\begin{itemize}
+		\item $\text{dom } f := \text{dom}(f) := \text{Definitionsbereich von } f := X$ Der Definitonsbereich sind die Werte von $x$, welche für diese Funktion erlaubt sind.
+		\item $\text{codom } f := \text{codom}(f) := \text{Zielbereich von } f := Y$ Der Zielbereich sind die Werte von $y$, welche für diese Funktion erlaubt sind.
+		\item Graph von $f := G$
+		\item Wert von $f$ an der Stelle $x \in X := f(x) := y$
+		\item $f : X \rightarrow Y := "\text{dom } f = X \text{und codom } f = Y"$
+	\end{itemize}
+}
+
+\dfn{Bild}{
+	Das Bild einer Funktion $f$ ist eine Menge, welche die möglichen $\text{codom}(f)$ beinhaltet ($\text{im}(f) \subseteq \text{codom}(f)$).
+
+	\[
+		f(A) := \{ f(x) | x \in A\}
+		.\]
+
+	Was bedeutet das? Wenn wir die Menge $A$, welches eine Teilmenge von $X$ ist, auf $f$ verwenden, so bekommen wir ein Teil, gegebenenfalls alle Elemente von $Y$.
+}
+
+\dfn{Urbild}{
+	Das Urbild einer Funktion $f$ ist eine Menge, welche die möglichen $\text{dom}(f)$ beinhaltet ($f ^{-1} \subseteq \text{dom}(f)$)
+
+	\[
+		f ^{-1} (B) := \{ x \in X | f(x) \in B \}
+		.\]
+
+	Was bedeutet das? Wenn wir die Menge $B$, welches eine Teilmenge von $Y$ ist, auf die Inverse von $f$ ($f ^{-1}$) verwenden, so bekommen wir ein Teil, gegebenenfalls alle Elemente von $X$.
+}
+
+Wir werden nun weitere Eigenschaften von Funktionen kennenlernen: Die Injektivität, Surjektivität und Bijektivität.
+
+\dfn{Injektiv}{
+	Eine Funktion ist injektiv wenn
+
+	\[
+		\forall x , x' \in X : f(x) = f(x') \Rightarrow x = x'
+		.\]
+
+	Einfach gesagt bedeutet dies, dass ein Element von $X$ nicht dasselbe Resultat ausgibt, wenn das Element in die Funktion eingesetzt wird.
+}
+
+\dfn{Surjektiv}{
+	Eine Funktion ist surjektiv wenn
+
+	\[
+		\forall y \in Y \exists x \in X : f(x) = y
+		.\]
+
+	Einfach gesagt bedeutet dies, dass ein Element von Y durch ein Element von X zugeordent ist. Dabei kann ein Element von X auch mehrere Elemente von Y zugeordnet sein.
+}
+
+\dfn{Bijektiv}{
+	Eine Funktion ist bijektiv wenn sie injektiv und surjektiv ist. Mathematisch bedeutet dies
+
+	\[
+		(\forall x , x' \in X : f(x) = f(x') \Rightarrow x = x') \land (\forall y \in Y \exists x \in X : f(x) = y)
+		.\]
+
+}
+
+\exa{injektiv, surjektiv, bijektiv \cite{Ziltner2024}}{
+	\begin{itemize}
+		\item Die Identität $\text{id}_x$ ist bijektiv
+		\item Die Funktion $f : [ 0, \infty ) \rightarrow \mathbb{R}, f(x) := x$, ist injektiv und nicht surjektiv.
+		\item Die Funktion $f :\mathbb{R} \rightarrow [ 0, \infty ) , f(x) := x ^2$, sit nicht injektiv, aber surjektiv.
+		\item Die Funktion $f : \mathbb{R} \rightarrow \mathbb{R}, f(x) := x ^2$, ist weder injektiv noch surjektiv.
+	\end{itemize}
+}
+
+\nt{
+	Die Identität ist eine Funktion welches sich selber wieder ausgibt.
+
+	\[
+		f(x) = x
+		.\]
+
+}
+
+\dfn{Umkehrfunktion / Inverse}{
+	Die Umkehrfunktion oder Inverse einer Funktion ist eine Funktion, welches das Gegenteil der Ursprünglichen Funktion $f$ macht.
+
+	\[
+		f ^{(-1)} : Y \rightarrow X, f ^{(-1)}(y) := x
+		.\]
+
+	In anderen Worten: wenn man ein Element von X in die Funktion einsetzt, so bekommt man ein Element von Y. Wichtig zu erwähnen ist, dass eine Inverse nur existiert, wenn die Funktion bijektiv ist.
+}
+
+\exa{Umkehrfunktion / Inverse \cite{Ziltner2024}}{
+	\begin{itemize}
+		\item Die Umkehrfunktion der Identität $\text{id}_x$ ist $\text{id}_x ^{-1} = \text{id}_x$.
+		\item Die Funktion $f : [ 0 , \infty ) , f(x) := x ^2$, ist bijektiv. Ihre Umkehrfunktion ist die Quadratwurzelfunktion $\sqrt{} := f ^{-1} : [ 0, \infty) \rightarrow [ 0 , \infty)$.
+		\item Die Exponentialfunktion exp als Funktion von $X := \mathbb{R}$ nach $Y := (0, \infty)$ ist bijektiv. Ihre Umkehrfunktion ist der natürliche Logarithmus $\text{log} := \text{exp} ^{-1} : (0, \infty) \rightarrow \mathbb{R}$.
+	\end{itemize}
+}
+
+\dfn{Verknüpfung von Funktionen}{
+	Die Verknüpfung von Funktion ist wie folgt definiert.
+
+	\[
+		g \circ f : X \rightarrow Z, g \circ f(x) := g(f(x))
+		.\]
+
+	Dies bdeuetet nichts weiter, dass der codom($f$) in die Funktion $g$ eingesetzt wird, und ELemente von $Z$ dabei herauskommen.
+	\\
+	Wichtig zu erwähnen ist, dass die codom($f$) = dom($g$) ist weil sonst die Verknüpfung nicht funktionieren würde.
+}
+
+\exa{Verknüpfung, Reihenfolge davon \cite{Ziltner2024}}{
+	\begin{itemize}
+		\item Wir betrachten $X := Y := Z$ und die Funktionen
+
+		      \[
+			      f, g : \mathbb{R} \rightarrow \mathbb{R}, f(x) := x + 1, g(y) := y ^2
+			      .\]
+
+		      Die Verknüpfung von $f$ und $g$ ist gegeben durch
+
+		      \[
+			      g \circ f : \mathbb{R} \rightarrow \mathbb{R}, g \circ f(x) = (x + 1) ^2
+			      .\]
+
+		      Der Zielbereich von $g$ ist gleich $\mathbb{R}$. Das stimmt mit dem Definitionsbereich von $f$ überein. Daher ist die umgekehrte Verknüpfung ebenfalls sinnvoll. Sie ist gegeben durch
+
+		      \[
+			      f \circ g : \mathbb{R} \rightarrow \mathbb{R}, f \circ g(y) = y ^2 + 1
+			      .\]
+
+		      In diesem Beispiel gilt daher
+
+		      \[
+			      g \circ f \neq f \circ g
+			      .\]
+
+		\item Wir betrachten $X := \mathbb{R} ^2, Y := Z := \mathbb{R}$ und die Funktionen
+
+		      \[
+			      f : \mathbb{R}^2 \rightarrow \mathbb{R}, f(x,y) := x + y, g := \text{exp} : \mathbb{R} \rightarrow \mathbb{R}
+			      .\]
+
+		      Die Verknüpfung von $f$ und $g$ ist gegeben durch
+
+		      \[
+			      g \circ f : \mathbb{R} ^2 \rightarrow \mathbb{R}, g \circ f(x,y) = \text{exp}(x + y) = e ^{x + y}
+			      .\]
+
+		      Die umgekehrte Verknüpfung $f \circ g$ ist nicht wohldefiniert (= sinnvoll), da der Yielbereich von $g$, also $\mathbb{R}$, nivcht gleich  dem Definitionsbereich von $f$, also $\mathbb{R} ^2$, ist.
+	\end{itemize}
+}

fs25/analysis_I_II/grundlagen/grundlagen.tex

@@ -1,3 +1,6 @@
 \chapter{Grundlagen: Logik, Mengen, Funktionen}
 
 \input{logik.tex}
+\input{mengenlehre.tex}
+\input{quantoren.tex}
+\input{funktionen.tex}

fs25/analysis_I_II/grundlagen/logik.tex

@@ -1,4 +1,4 @@
-\section{Logik}
+\section{Logik} \label{cha:logic}
 
 \subsection{Grundlagen}
 

fs25/analysis_I_II/grundlagen/mengenlehre.tex

@@ -0,0 +1,168 @@
+\section{Mengenlehre}
+
+\subsection{Grundlagen}
+
+Eine Menge ist eine ungeordnete Zusammenfassung von Objekten zu einem Ganzen. Die in einer Menge enthaltenen Objekte nennen wir ihre Elemente. \cite{Ziltner2024}
+\\
+\\
+\thm{Schreibweise einer Menge}{
+	Nehmen wir an, dass $x_1, x_2, ... x_{n}$ Elemente sind. Dann ist die Menge, bestehend aus den Elementen $x_1, x_2, ... x_{n}$
+
+	\[
+		\{ x_1, x_2, ... x_{n} \}
+		.\]
+}
+
+\exa{}{
+	\begin{itemize}
+		\item $\{ 1,0 \}$
+		\item $\emptyset$
+		\item $\{ \emptyset \}$
+	\end{itemize}
+}
+
+\nt{
+	Mengen können wiederholende Elemente besitzen.
+}
+
+\dfn{Beschreibende Mengenschreibweise}{
+	Die beschreibende Mengenschreibweise ist eine Aussageform, welche Elemente $x$ definiert, die in einer Menge enthalten sein können und eine Bedingung $P(x)$ erfüllen.
+
+	\begin{equation}
+		\{ x | P(x) \} \text{Für die Menge aller $x$, für die $P(x)$ gilt.}
+	\end{equation}
+}
+
+\exa{}{
+	\begin{itemize}
+		\item $\{ n | n \in \mathbb{N}_0 : n \text{ ist gerade} \}$
+	\end{itemize}
+}
+
+\subsection{Mengenoperationen und Teilmengenrelation}
+
+Wie in Kapitel \ref{cha:logic} haben Mengen auch Logikoperationen. Sie sind sehr ähnlich zu den "normalen" Logikoperationen.
+
+\begin{tabular}{ c  c }
+	$A \cup B$      & $\{ x | x \in A \land x \in B \}$ = Durchschnitt \\
+	$A \cap B$      & $\{ x | x \in A \lor x \in B \}$ = Vereinigung   \\
+	$A \setminus B$ & $\{ x \in A | x \notin B \}$ = Differenz         \\
+\end{tabular}
+
+Wenn die Menge $A$ auch in der Menge $B$ liegt, so ist $A$ eine Teilmenge von $B$.
+
+\[
+	A \subseteq B
+	.\]
+
+\thm{Das Komplementär einer Menge}{
+	Das Komplementär einer Menge definiert eine Menge $A$, welche die Elemente einer anderen Menge $B$ nicht beinhaltet.
+
+	\[
+		B ^{\complement} = A \setminus B
+		.\]
+}
+
+\thm{De-Morganschen Gesetze}{
+	\begin{itemize}
+		\item $(A \cup B)^\complement = A ^\complement \cap B ^\complement$
+		\item $( A \cap B ) ^\complement = A ^\complement \cup B ^\complement$
+	\end{itemize}
+}
+
+\thm{Tupel}{
+	Wenn wir eine Liste von Elementen, bestehen aus $x_1, ..., x_{n}$ haben, so nennen wir diese Liste ein Tupel. Die Anzahl von Elementen $n$ sowie die Anordunng der Elementen spielt eine Rolle.
+
+	\begin{itemize}
+		\item Für $n = 2$ nennen wir den Tupel ein Paar.
+		\item Für $n = 3$ nennen wir den Tupel ein Trippel.
+		\item Für alle anderen $n$ bezeichnet man die Liste als n-Tupel.
+	\end{itemize}
+
+	Wie schon vorher erwähnt spielt die Anordung eine grosse Rolle. ($(x_1, x_2) \neq (x_2, x_1)$)
+}
+
+\thm{Karthesisches Produkt}{
+	Das Produkt zweier Mengen (\textit{karthesische Produkt}) $X$ und $Y$ kann als eine Menge bestehend aus den Permutationen den Elementen der beiden Mengen dargestellt werden.
+}
+
+\exa{Karthesisches Produkt}{
+	Sei $X := \{ 0,1 \}$ und $Y := \{ \text{Apfel}, \text{Berg} \}$.
+
+	\[
+		X \times Y  = \{ (0,\text{Apfel}), (0,\text{Berg}), (1, \text{Apfel}), (1, \text{Berg}) \}
+		.\]
+}
+
+\nt{
+	Für Potenzen gilt das gleiche Prinzip, i.e $X ^{2} = X \times X$, $X ^{3} = (X \times X) \times X$, usw.
+}
+
+\dfn{Euklidische Norm}{
+Die euklidische Norm $|| \cdot ||$ ist die Distanz von einem Punkt, z.B. $\nu$ zu ihrem Ursprung und wird wie folgt berechnet.
+
+\[
+	||\nu|| := \sqrt{\sum_{i = 1}^{n}v_i ^{2}}
+	.\]
+
+}
+
+\newpage
+
+\thm{Offener und abgeschlossener Ball, Sphäre}{
+	E
+	in Ball oder eine Sphäre ist eine Menge von Punkten in einen $n$-Dimensionalen Raum, welche einen bestimmten Abstand zum Mittelpunkt des Balles bzw. der Sphäre haben.
+
+	\begin{enumerate}
+		\item Der offene Ball ist eine Menge von Punkten, deren Abstand zum Mittelpunkt $x_0$ kleiner als der Radius $r$ ist.
+
+		      \[
+			      B_r(x_0) := B ^{n} _r(x_0) := \{ x \in \mathbb{R} ^{n} | ||x-x_0|| < r \}
+			      .\]
+
+		\item Der abgeschlossene Ball ist eine Menge von Punkten, deren Abstand zum Mittelpunkt $x_0$ kleiner oder gleich dem Radius ist.
+
+		      \[
+			      \bar{B}_r(x_0) := \bar{B} ^{n} _r(x_0) := \{ x \in \mathbb{R} ^{n} | ||x - x_0|| \leq r \}
+			      .\]
+
+		\item Die Sphäre ist eine Menge von Punkten, deren Abstand zum Mittelpunkt $x_0$ gleich dem Radius ist.
+
+		      \[
+			      S ^{n-1} _r (x_0) := \{ x \in \mathbb{R}^{n}| ||x - x_0|| = r \}
+			      .\]
+	\end{enumerate}
+
+
+}
+
+\begin{figure}[h]
+	\begin{center}
+		\includegraphics[width=\textwidth]{fig/Fig_1.png}
+	\end{center}
+	\caption{Von links nach rechts: Offener Ball, abgeschlossener Ball, Sphäre}
+\end{figure}
+
+\nt{
+	Das die Sphäre eine Dimension verliert ($n-1$) ist auf dem ersten Blick verwirrend, macht aber Sinn. Bei einer Sphäre wird nur der Mantel betrachtet. Dadurch wird der Freiheitsgrad verringert was dazu führt, dass eine Dimension verloren geht i.e. der Mantel einer Kugel ist eine Fläche oder der Rand einer Kreisscheibe ist eine Linie.
+}
+
+\thm{Fall $r = 0$ und $r = \infty$}{
+	Falls $r = 0$ gilt für den Ball
+	\begin{itemize}
+		\item $B_0(x_0) = \emptyset$ da die euklidische Norm nicht kleiner als 0 sein kann
+		\item $\bar{B}_0(x_0) = \{ x_0 \}$ da der einzige Punkt dessen Abstand zum Mittelpunkt null ist der Mittelpunkt selbst ist.
+	\end{itemize}
+
+	Falls $r = \infty$, dann gilt
+
+	\begin{itemize}
+		\item $B_{\infty}(x_0) = \mathbb{R} ^{n}$
+		\item $\bar{B}_{\infty}(x_0) = \mathbb{R} ^{n}$
+	\end{itemize}
+}
+
+\nt{
+	Obwohl $\mathbb{R}^{n}$ ein offener und auch ein geschlossener Ball sein kann bedeutet es nicht, dass $B_{\infty} (x_0) = \bar{B}_{\infty} (x_0)$ ist. Das Problem ist, dass kein Rand existiert für einen Kreis mit $r = \infty$. Deshalb ist $\mathbb{R}^{n}$ beides.
+}
+

fs25/analysis_I_II/grundlagen/quantoren.tex

@@ -0,0 +1,38 @@
+\section{Quantoren}
+
+Quantoren sind logische Operatoren, die angeben, wie viele Objekte $x$ eine Bedingung $P(x)$ erfüllen. Die zwei wichtigsten Quantoren sind die folgenden: \cite{Ziltner2024}
+
+\begin{center}
+	\begin{tabular}{| c | c | c |}
+		Notation  & Bedeutung                & Beziehung       \\
+		\hline
+		$\forall$ & "für jedes" = "für alle" & Allquantor      \\
+		$\exists$ & "es gibt"                & Existenzquantor \\
+	\end{tabular}
+	\\
+	\cite{Ziltner2024}
+\end{center}
+
+\exa{Quantoren}{
+	\begin{itemize}
+		\item[(i)] $\forall n \in \mathbb{N}_0 : n \geq 0$ ist Wahr
+		\item[(ii)] $\exists n \in \mathbb{N}_0 : n > 0$ ist Wahr
+		\item[(iii)] $\forall m \in \mathbb{N}_0 \exists n \in \mathbb{N}_0 : m \leq n$ ist Wahr
+		\item[(iv)] $\exists n \in \mathbb{N}_0 \forall m \in \mathbb{N}_0 : m \leq n$ ist Falsch
+	\end{itemize}
+}
+
+\nt{
+	Die Reihenfolge der Quantoren spielt eine Rolle. Dies können wir an den vorheringen Beispielen erkennen.
+}
+
+\thm{Verneinung einer quantifizierten Assageform}{
+	Die Verneinung von den Quantoren $\forall$ und $\exists$ ist wie folgt definiert.
+
+	\[
+		\neg(\forall x \in X : P(x)) \equiv \exists x \in X : \neg P(x)
+		.\]
+	\[
+		\neg(\exists x \in X : P(x)) \equiv \forall x \in X : \neg P(x)
+		.\]
+}

fs25/analysis_I_II/vektorfeld/satz_green.aux

@@ -0,0 +1,62 @@
+\relax 
+\providecommand{\transparent@use}[1]{}
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {section}{\numberline {12.1}Satz von Green}{27}{section.12.1}\protected@file@percent }
+\@setckpt{./vektorfeld/./satz_green}{
+\setcounter{page}{28}
+\setcounter{equation}{0}
+\setcounter{enumi}{3}
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+}

fs25/analysis_I_II/vektorfeld/satz_green.tex

@@ -0,0 +1,26 @@
+\section{Satz von Green}
+
+% Notiz zu Satz von Stokes
+
+\nt{
+	Der intrinsische Rand ist nicht dasselbe wie der topologische Rand. Wenn wir einen Halbkreis in einem Raum betrachten, so ist der topologische Rand die Gerade des Halbkreises, sowie die gebogene Gerade. Der intrinsische Rand betrachtet nur die Gerade.
+}
+
+% Notiz zu Satz von Stokes
+
+\nt{
+	$\text{rot } X$ ist eine stetige Funktion. Was dies besagt ist, dass wenn das Intervall $x_j$ immer kleiner gewählt wird, so kommt man immer näher an den Mittelwert der Funktion.
+}
+
+% Notiz zu parametrisierbare Untermannigfaltigkeit
+
+\nt{
+	$C^k$ Einbettung, weil wir dadurch die Topologie beibehalten. Ohne der Einbettung würden wir die Form abändern.
+}
+
+% Notiz zu Einheitsnormalvektorfeld
+
+\nt{
+	Der Einheitsnormalvektorfeld beschreibt, wie die Fläche eines Körper orientiert ist. Wenn wir an jedem Punkt eines Körpers eine Tangentialfläche projezieren und an jeder Tangentialfläche einen Normalvektor hinzufügen, so bilden wir den Einheitsnormalvektorfeld. Die Koorentierung sorgt einfach dafür, dass der Einheitsnormalvektor nach aussen zeigt.
+}
+

fs25/analysis_I_II/vektorfeld/vektorfeld.tex

@@ -1 +1,3 @@
 \chapter{Vektorfelder und die Sätze von Green, Stokes und Gauss}
+
+\include{./satz_green.tex}

fs25/mathematische_methoden/fourier_analysis/fourier_analysis.tex

@@ -0,0 +1 @@
+\chapter{Fourier Analysis}

fs25/mathematische_methoden/komplexe_zahlen/komplexe_zahlen.tex

@@ -0,0 +1 @@
+\chapter{Komplexe Zahlen}

fs25/mathematische_methoden/komplexwertige_funktionen/komplexwertige_funktionen.tex

@@ -0,0 +1 @@
+\chapter{Komplexwertige Funktionen}

fs25/mathematische_methoden/laplace_transformation/laplace_transformation.tex

@@ -0,0 +1 @@
+\chapter{Laplace-Transformation}

fs25/mathematische_methoden/letterfonts.tex

@@ -0,0 +1,178 @@
+% Things Lie
+\newcommand{\kb}{\mathfrak b}
+\newcommand{\kg}{\mathfrak g}
+\newcommand{\kh}{\mathfrak h}
+\newcommand{\kn}{\mathfrak n}
+\newcommand{\ku}{\mathfrak u}
+\newcommand{\kz}{\mathfrak z}
+\DeclareMathOperator{\Ext}{Ext} % Ext functor
+\DeclareMathOperator{\Tor}{Tor} % Tor functor
+\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group
+\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6
+
+% More script letters etc.
+\newcommand{\SA}{\mathcal A}
+\newcommand{\SB}{\mathcal B}
+\newcommand{\SC}{\mathcal C}
+\newcommand{\SF}{\mathcal F}
+\newcommand{\SG}{\mathcal G}
+\newcommand{\SH}{\mathcal H}
+\newcommand{\OO}{\mathcal O}
+
+\newcommand{\SCA}{\mathscr A}
+\newcommand{\SCB}{\mathscr B}
+\newcommand{\SCC}{\mathscr C}
+\newcommand{\SCD}{\mathscr D}
+\newcommand{\SCE}{\mathscr E}
+\newcommand{\SCF}{\mathscr F}
+\newcommand{\SCG}{\mathscr G}
+\newcommand{\SCH}{\mathscr H}
+
+% Mathfrak primes
+\newcommand{\km}{\mathfrak m}
+\newcommand{\kp}{\mathfrak p}
+\newcommand{\kq}{\mathfrak q}
+
+% number sets
+\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}}
+\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}}
+\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}}
+\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}}
+\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}}
+\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}}
+\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}}
+\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}}
+% expected value
+\newcommand{\EE}{\ensuremath{\mathbb{E}}}
+\newcommand{\charin}{\text{ char }}
+\DeclareMathOperator{\sign}{sign}
+\DeclareMathOperator{\Aut}{Aut}
+\DeclareMathOperator{\Inn}{Inn}
+\DeclareMathOperator{\Syl}{Syl}
+\DeclareMathOperator{\Gal}{Gal}
+\DeclareMathOperator{\GL}{GL} % General linear group
+\DeclareMathOperator{\SL}{SL} % Special linear group
+
+%---------------------------------------
+% BlackBoard Math Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\bbA}{\mathbb{A}}	\newcommand{\bbB}{\mathbb{B}}
+\newcommand{\bbC}{\mathbb{C}}	\newcommand{\bbD}{\mathbb{D}}
+\newcommand{\bbE}{\mathbb{E}}	\newcommand{\bbF}{\mathbb{F}}
+\newcommand{\bbG}{\mathbb{G}}	\newcommand{\bbH}{\mathbb{H}}
+\newcommand{\bbI}{\mathbb{I}}	\newcommand{\bbJ}{\mathbb{J}}
+\newcommand{\bbK}{\mathbb{K}}	\newcommand{\bbL}{\mathbb{L}}
+\newcommand{\bbM}{\mathbb{M}}	\newcommand{\bbN}{\mathbb{N}}
+\newcommand{\bbO}{\mathbb{O}}	\newcommand{\bbP}{\mathbb{P}}
+\newcommand{\bbQ}{\mathbb{Q}}	\newcommand{\bbR}{\mathbb{R}}
+\newcommand{\bbS}{\mathbb{S}}	\newcommand{\bbT}{\mathbb{T}}
+\newcommand{\bbU}{\mathbb{U}}	\newcommand{\bbV}{\mathbb{V}}
+\newcommand{\bbW}{\mathbb{W}}	\newcommand{\bbX}{\mathbb{X}}
+\newcommand{\bbY}{\mathbb{Y}}	\newcommand{\bbZ}{\mathbb{Z}}
+
+%---------------------------------------
+% MathCal Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\mcA}{\mathcal{A}}	\newcommand{\mcB}{\mathcal{B}}
+\newcommand{\mcC}{\mathcal{C}}	\newcommand{\mcD}{\mathcal{D}}
+\newcommand{\mcE}{\mathcal{E}}	\newcommand{\mcF}{\mathcal{F}}
+\newcommand{\mcG}{\mathcal{G}}	\newcommand{\mcH}{\mathcal{H}}
+\newcommand{\mcI}{\mathcal{I}}	\newcommand{\mcJ}{\mathcal{J}}
+\newcommand{\mcK}{\mathcal{K}}	\newcommand{\mcL}{\mathcal{L}}
+\newcommand{\mcM}{\mathcal{M}}	\newcommand{\mcN}{\mathcal{N}}
+\newcommand{\mcO}{\mathcal{O}}	\newcommand{\mcP}{\mathcal{P}}
+\newcommand{\mcQ}{\mathcal{Q}}	\newcommand{\mcR}{\mathcal{R}}
+\newcommand{\mcS}{\mathcal{S}}	\newcommand{\mcT}{\mathcal{T}}
+\newcommand{\mcU}{\mathcal{U}}	\newcommand{\mcV}{\mathcal{V}}
+\newcommand{\mcW}{\mathcal{W}}	\newcommand{\mcX}{\mathcal{X}}
+\newcommand{\mcY}{\mathcal{Y}}	\newcommand{\mcZ}{\mathcal{Z}}
+
+
+%---------------------------------------
+% Bold Math Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\bmA}{\boldsymbol{A}}	\newcommand{\bmB}{\boldsymbol{B}}
+\newcommand{\bmC}{\boldsymbol{C}}	\newcommand{\bmD}{\boldsymbol{D}}
+\newcommand{\bmE}{\boldsymbol{E}}	\newcommand{\bmF}{\boldsymbol{F}}
+\newcommand{\bmG}{\boldsymbol{G}}	\newcommand{\bmH}{\boldsymbol{H}}
+\newcommand{\bmI}{\boldsymbol{I}}	\newcommand{\bmJ}{\boldsymbol{J}}
+\newcommand{\bmK}{\boldsymbol{K}}	\newcommand{\bmL}{\boldsymbol{L}}
+\newcommand{\bmM}{\boldsymbol{M}}	\newcommand{\bmN}{\boldsymbol{N}}
+\newcommand{\bmO}{\boldsymbol{O}}	\newcommand{\bmP}{\boldsymbol{P}}
+\newcommand{\bmQ}{\boldsymbol{Q}}	\newcommand{\bmR}{\boldsymbol{R}}
+\newcommand{\bmS}{\boldsymbol{S}}	\newcommand{\bmT}{\boldsymbol{T}}
+\newcommand{\bmU}{\boldsymbol{U}}	\newcommand{\bmV}{\boldsymbol{V}}
+\newcommand{\bmW}{\boldsymbol{W}}	\newcommand{\bmX}{\boldsymbol{X}}
+\newcommand{\bmY}{\boldsymbol{Y}}	\newcommand{\bmZ}{\boldsymbol{Z}}
+%Small Letters
+\newcommand{\bma}{\boldsymbol{a}}	\newcommand{\bmb}{\boldsymbol{b}}
+\newcommand{\bmc}{\boldsymbol{c}}	\newcommand{\bmd}{\boldsymbol{d}}
+\newcommand{\bme}{\boldsymbol{e}}	\newcommand{\bmf}{\boldsymbol{f}}
+\newcommand{\bmg}{\boldsymbol{g}}	\newcommand{\bmh}{\boldsymbol{h}}
+\newcommand{\bmi}{\boldsymbol{i}}	\newcommand{\bmj}{\boldsymbol{j}}
+\newcommand{\bmk}{\boldsymbol{k}}	\newcommand{\bml}{\boldsymbol{l}}
+\newcommand{\bmm}{\boldsymbol{m}}	\newcommand{\bmn}{\boldsymbol{n}}
+\newcommand{\bmo}{\boldsymbol{o}}	\newcommand{\bmp}{\boldsymbol{p}}
+\newcommand{\bmq}{\boldsymbol{q}}	\newcommand{\bmr}{\boldsymbol{r}}
+\newcommand{\bms}{\boldsymbol{s}}	\newcommand{\bmt}{\boldsymbol{t}}
+\newcommand{\bmu}{\boldsymbol{u}}	\newcommand{\bmv}{\boldsymbol{v}}
+\newcommand{\bmw}{\boldsymbol{w}}	\newcommand{\bmx}{\boldsymbol{x}}
+\newcommand{\bmy}{\boldsymbol{y}}	\newcommand{\bmz}{\boldsymbol{z}}
+
+%---------------------------------------
+% Scr Math Fonts :-
+%---------------------------------------
+
+\newcommand{\sA}{{\mathscr{A}}}   \newcommand{\sB}{{\mathscr{B}}}
+\newcommand{\sC}{{\mathscr{C}}}   \newcommand{\sD}{{\mathscr{D}}}
+\newcommand{\sE}{{\mathscr{E}}}   \newcommand{\sF}{{\mathscr{F}}}
+\newcommand{\sG}{{\mathscr{G}}}   \newcommand{\sH}{{\mathscr{H}}}
+\newcommand{\sI}{{\mathscr{I}}}   \newcommand{\sJ}{{\mathscr{J}}}
+\newcommand{\sK}{{\mathscr{K}}}   \newcommand{\sL}{{\mathscr{L}}}
+\newcommand{\sM}{{\mathscr{M}}}   \newcommand{\sN}{{\mathscr{N}}}
+\newcommand{\sO}{{\mathscr{O}}}   \newcommand{\sP}{{\mathscr{P}}}
+\newcommand{\sQ}{{\mathscr{Q}}}   \newcommand{\sR}{{\mathscr{R}}}
+\newcommand{\sS}{{\mathscr{S}}}   \newcommand{\sT}{{\mathscr{T}}}
+\newcommand{\sU}{{\mathscr{U}}}   \newcommand{\sV}{{\mathscr{V}}}
+\newcommand{\sW}{{\mathscr{W}}}   \newcommand{\sX}{{\mathscr{X}}}
+\newcommand{\sY}{{\mathscr{Y}}}   \newcommand{\sZ}{{\mathscr{Z}}}
+
+
+%---------------------------------------
+% Math Fraktur Font
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\mfA}{\mathfrak{A}}	\newcommand{\mfB}{\mathfrak{B}}
+\newcommand{\mfC}{\mathfrak{C}}	\newcommand{\mfD}{\mathfrak{D}}
+\newcommand{\mfE}{\mathfrak{E}}	\newcommand{\mfF}{\mathfrak{F}}
+\newcommand{\mfG}{\mathfrak{G}}	\newcommand{\mfH}{\mathfrak{H}}
+\newcommand{\mfI}{\mathfrak{I}}	\newcommand{\mfJ}{\mathfrak{J}}
+\newcommand{\mfK}{\mathfrak{K}}	\newcommand{\mfL}{\mathfrak{L}}
+\newcommand{\mfM}{\mathfrak{M}}	\newcommand{\mfN}{\mathfrak{N}}
+\newcommand{\mfO}{\mathfrak{O}}	\newcommand{\mfP}{\mathfrak{P}}
+\newcommand{\mfQ}{\mathfrak{Q}}	\newcommand{\mfR}{\mathfrak{R}}
+\newcommand{\mfS}{\mathfrak{S}}	\newcommand{\mfT}{\mathfrak{T}}
+\newcommand{\mfU}{\mathfrak{U}}	\newcommand{\mfV}{\mathfrak{V}}
+\newcommand{\mfW}{\mathfrak{W}}	\newcommand{\mfX}{\mathfrak{X}}
+\newcommand{\mfY}{\mathfrak{Y}}	\newcommand{\mfZ}{\mathfrak{Z}}
+%Small Letters
+\newcommand{\mfa}{\mathfrak{a}}	\newcommand{\mfb}{\mathfrak{b}}
+\newcommand{\mfc}{\mathfrak{c}}	\newcommand{\mfd}{\mathfrak{d}}
+\newcommand{\mfe}{\mathfrak{e}}	\newcommand{\mff}{\mathfrak{f}}
+\newcommand{\mfg}{\mathfrak{g}}	\newcommand{\mfh}{\mathfrak{h}}
+\newcommand{\mfi}{\mathfrak{i}}	\newcommand{\mfj}{\mathfrak{j}}
+\newcommand{\mfk}{\mathfrak{k}}	\newcommand{\mfl}{\mathfrak{l}}
+\newcommand{\mfm}{\mathfrak{m}}	\newcommand{\mfn}{\mathfrak{n}}
+\newcommand{\mfo}{\mathfrak{o}}	\newcommand{\mfp}{\mathfrak{p}}
+\newcommand{\mfq}{\mathfrak{q}}	\newcommand{\mfr}{\mathfrak{r}}
+\newcommand{\mfs}{\mathfrak{s}}	\newcommand{\mft}{\mathfrak{t}}
+\newcommand{\mfu}{\mathfrak{u}}	\newcommand{\mfv}{\mathfrak{v}}
+\newcommand{\mfw}{\mathfrak{w}}	\newcommand{\mfx}{\mathfrak{x}}
+\newcommand{\mfy}{\mathfrak{y}}	\newcommand{\mfz}{\mathfrak{z}}

fs25/mathematische_methoden/macros.tex

@@ -0,0 +1,88 @@
+%From M275 "Topology" at SJSU
+\newcommand{\id}{\mathrm{id}}
+\newcommand{\taking}[1]{\xrightarrow{#1}}
+\newcommand{\inv}{^{-1}}
+
+%From M170 "Introduction to Graph Theory" at SJSU
+\DeclareMathOperator{\diam}{diam}
+\DeclareMathOperator{\ord}{ord}
+\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
+
+%From the USAMO .tex files
+\newcommand{\ts}{\textsuperscript}
+\newcommand{\dg}{^\circ}
+\newcommand{\ii}{\item}
+
+% % From Math 55 and Math 145 at Harvard
+% \newenvironment{subproof}[1][Proof]{%
+% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}%
+% {\end{proof}}
+
+\newcommand{\liff}{\leftrightarrow}
+\newcommand{\lthen}{\rightarrow}
+\newcommand{\opname}{\operatorname}
+\newcommand{\surjto}{\twoheadrightarrow}
+\newcommand{\injto}{\hookrightarrow}
+\newcommand{\On}{\mathrm{On}} % ordinals
+\DeclareMathOperator{\img}{im} % Image
+\DeclareMathOperator{\Img}{Im} % Image
+\DeclareMathOperator{\coker}{coker} % Cokernel
+\DeclareMathOperator{\Coker}{Coker} % Cokernel
+\DeclareMathOperator{\Ker}{Ker} % Kernel
+\DeclareMathOperator{\rank}{rank}
+\DeclareMathOperator{\Spec}{Spec} % spectrum
+\DeclareMathOperator{\Tr}{Tr} % trace
+\DeclareMathOperator{\pr}{pr} % projection
+\DeclareMathOperator{\ext}{ext} % extension
+\DeclareMathOperator{\pred}{pred} % predecessor
+\DeclareMathOperator{\dom}{dom} % domain
+\DeclareMathOperator{\ran}{ran} % range
+\DeclareMathOperator{\Hom}{Hom} % homomorphism
+\DeclareMathOperator{\Mor}{Mor} % morphisms
+\DeclareMathOperator{\End}{End} % endomorphism
+
+\newcommand{\eps}{\epsilon}
+\newcommand{\veps}{\varepsilon}
+\newcommand{\ol}{\overline}
+\newcommand{\ul}{\underline}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+\newcommand{\vocab}[1]{\textbf{\color{blue} #1}}
+\providecommand{\half}{\frac{1}{2}}
+\newcommand{\dang}{\measuredangle} %% Directed angle
+\newcommand{\ray}[1]{\overrightarrow{#1}}
+\newcommand{\seg}[1]{\overline{#1}}
+\newcommand{\arc}[1]{\wideparen{#1}}
+\DeclareMathOperator{\cis}{cis}
+\DeclareMathOperator*{\lcm}{lcm}
+\DeclareMathOperator*{\argmin}{arg min}
+\DeclareMathOperator*{\argmax}{arg max}
+\newcommand{\cycsum}{\sum_{\mathrm{cyc}}}
+\newcommand{\symsum}{\sum_{\mathrm{sym}}}
+\newcommand{\cycprod}{\prod_{\mathrm{cyc}}}
+\newcommand{\symprod}{\prod_{\mathrm{sym}}}
+\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}}
+\newcommand{\parinn}{\setlength{\parindent}{1cm}}
+\newcommand{\parinf}{\setlength{\parindent}{0cm}}
+% \newcommand{\norm}{\|\cdot\|}
+\newcommand{\inorm}{\norm_{\infty}}
+\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}}
+\newcommand{\oset}{V_{\alpha}}
+\newcommand{\opset}[1]{V_{\alpha_{#1}}}
+\newcommand{\lub}{\text{lub}}
+\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}}
+\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}}
+\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}}
+\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}}
+\newcommand{\lm}{\lambda}
+\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}}
+\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}}
+\newcommand{\lt}{\left}
+\newcommand{\rt}{\right}
+\newcommand{\bs}[1]{\boldsymbol{#1}}
+\newcommand{\exs}{\exists}
+\newcommand{\st}{\strut}
+\newcommand{\dps}[1]{\displaystyle{#1}}
+
+\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
+\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}

fs25/mathematische_methoden/notizen_koma_ruh_jirayu.aux

@@ -0,0 +1,52 @@
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fs25/mathematische_methoden/notizen_koma_ruh_jirayu.fdb_latexmk

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+INPUT komplexwertige_funktionen/komplexwertige_funktionen.tex
+INPUT ./komplexwertige_funktionen/komplexwertige_funktionen.tex
+INPUT komplexwertige_funktionen/komplexwertige_funktionen.tex
+INPUT ./taylor_laurentreihen/taylor_laurentreihen.tex
+INPUT taylor_laurentreihen/taylor_laurentreihen.tex
+INPUT ./taylor_laurentreihen/taylor_laurentreihen.tex
+INPUT taylor_laurentreihen/taylor_laurentreihen.tex
+INPUT ./taylor_laurentreihen/reihen_entwicklung.tex
+OUTPUT taylor_laurentreihen/reihen_entwicklung.aux
+INPUT ./taylor_laurentreihen/reihen_entwicklung.tex
+INPUT ./taylor_laurentreihen/reihen_entwicklung.tex
+INPUT taylor_laurentreihen/reihen_entwicklung.tex
+INPUT taylor_laurentreihen/reihen_entwicklung.tex
+INPUT ./fourier_analysis/fourier_analysis.tex
+INPUT fourier_analysis/fourier_analysis.tex
+INPUT ./fourier_analysis/fourier_analysis.tex
+INPUT fourier_analysis/fourier_analysis.tex
+INPUT ./laplace_transformation/laplace_transformation.tex
+INPUT laplace_transformation/laplace_transformation.tex
+INPUT ./laplace_transformation/laplace_transformation.tex
+INPUT laplace_transformation/laplace_transformation.tex
+INPUT notizen_koma_ruh_jirayu.aux
+INPUT ./taylor_laurentreihen/reihen_entwicklung.aux
+INPUT ./taylor_laurentreihen/reihen_entwicklung.aux
+INPUT taylor_laurentreihen/reihen_entwicklung.aux
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb
+INPUT /usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb

fs25/mathematische_methoden/notizen_koma_ruh_jirayu.tex

@@ -0,0 +1,39 @@
+\documentclass{report}
+
+\def\papertitle{Notizen zu Mathematische Methoden (frühere Name: Komplexe Analysis)}
+
+\def\theorytitle{Theorie}
+\def\corollarytitle{Korollar}
+\def\proposaltitle{Vorschlag}
+\def\claimtitle{Behauptung}
+\def\exercisetitle{Aufgabe}
+\def\exampletitle{Beispiel}
+\def\questiontitle{Frage}
+\def\wrongctitle{Falscher Konzept}
+\def\pagetitle{Seite}
+\def\pagetitle{Kapitel}
+
+\input{preamble}
+\input{macros}
+\input{letterfonts}
+
+\title{\huge{\papertitle}}
+\author{\huge{Jirayu Ruh}}
+\date{}
+
+\begin{document}
+
+\maketitle
+\newpage% or \cleardoublepage
+% \pdfbookmark[<level>]{<title>}{<dest>}
+\pdfbookmark[section]{\contentsname}{toc}
+\tableofcontents
+\pagebreak
+
+\import{komplexe_zahlen}{komplexe_zahlen.tex}
+\import{komplexwertige_funktionen}{komplexwertige_funktionen.tex}
+\import{taylor_laurentreihen}{taylor_laurentreihen.tex}
+\import{fourier_analysis}{fourier_analysis.tex}
+\import{laplace_transformation}{laplace_transformation.tex}
+
+\end{document}

fs25/mathematische_methoden/notizen_koma_ruh_jirayu.toc

@@ -0,0 +1,8 @@
+\babel@toc {ngerman}{}\relax 
+\contentsline {chapter}{\numberline {1}Komplexe Zahlen}{2}{chapter.1}%
+\contentsline {chapter}{\numberline {2}Komplexwertige Funktionen}{3}{chapter.2}%
+\contentsline {chapter}{\numberline {3}Taylor- und Laurentreihen}{4}{chapter.3}%
+\contentsline {section}{\numberline {3.1}Reihen-Entwichlung}{5}{section.3.1}%
+\contentsline {chapter}{\numberline {4}Fourier Analysis}{6}{chapter.4}%
+\contentsline {chapter}{\numberline {5}Laplace-Transformation}{7}{chapter.5}%
+\contentsfinish 

fs25/mathematische_methoden/preamble.tex

@@ -0,0 +1,741 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% PACKAGE IMPORTS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% TODO: Uncomment if the paper is in German
+\usepackage[ngerman]{babel}
+\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry}
+\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools}
+\usepackage[varbb]{newpxmath}
+\usepackage{xfrac}
+\usepackage[makeroom]{cancel}
+\usepackage{mathtools}
+\usepackage{bookmark}
+\usepackage{enumitem}
+\usepackage{hyperref,theoremref}
+\hypersetup{
+	pdftitle={Assignment},
+	colorlinks=true, linkcolor=doc!90,
+	bookmarksnumbered=true,
+	bookmarksopen=true
+}
+\usepackage[most,many,breakable]{tcolorbox}
+\usepackage{xcolor}
+\usepackage{varwidth}
+\usepackage{varwidth}
+\usepackage{etoolbox}
+%\usepackage{authblk}
+\usepackage{nameref}
+\usepackage{multicol,array}
+\usepackage{tikz-cd}
+\usepackage[ruled,vlined,linesnumbered]{algorithm2e}
+\usepackage{comment} % enables the use of multi-line comments (\ifx \fi) 
+\usepackage{import}
+\usepackage{xifthen}
+\usepackage{pdfpages}
+\usepackage{transparent}
+
+\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}}
+\SetCommentSty{mycommfont}
+\newcommand{\incfig}[1]{%
+	\def\svgwidth{\columnwidth}
+	\import{./figures/}{#1.pdf_tex}
+}
+
+\usepackage{tikzsymbols}
+\renewcommand\qedsymbol{$\Laughey$}
+
+
+%\usepackage{import}
+%\usepackage{xifthen}
+%\usepackage{pdfpages}
+%\usepackage{transparent}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% SELF MADE COLORS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\definecolor{myg}{RGB}{56, 140, 70}
+\definecolor{myb}{RGB}{45, 111, 177}
+\definecolor{myr}{RGB}{199, 68, 64}
+\definecolor{mytheorembg}{HTML}{F2F2F9}
+\definecolor{mytheoremfr}{HTML}{00007B}
+\definecolor{mylenmabg}{HTML}{FFFAF8}
+\definecolor{mylenmafr}{HTML}{983b0f}
+\definecolor{mypropbg}{HTML}{f2fbfc}
+\definecolor{mypropfr}{HTML}{191971}
+\definecolor{myexamplebg}{HTML}{F2FBF8}
+\definecolor{myexamplefr}{HTML}{88D6D1}
+\definecolor{myexampleti}{HTML}{2A7F7F}
+\definecolor{mydefinitbg}{HTML}{E5E5FF}
+\definecolor{mydefinitfr}{HTML}{3F3FA3}
+\definecolor{notesgreen}{RGB}{0,162,0}
+\definecolor{myp}{RGB}{197, 92, 212}
+\definecolor{mygr}{HTML}{2C3338}
+\definecolor{myred}{RGB}{127,0,0}
+\definecolor{myyellow}{RGB}{169,121,69}
+\definecolor{myexercisebg}{HTML}{F2FBF8}
+\definecolor{myexercisefg}{HTML}{88D6D1}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% TCOLORBOX SETUPS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\setlength{\parindent}{0cm}
+
+%================================
+% THEOREM BOX
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{Theorem}{\theorytitle}
+{%
+	enhanced,
+	breakable,
+	colback = mytheorembg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mytheoremfr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mytheoremfr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mytheoremfr},
+}
+{th}
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=chapter]{theorem}{\theorytitle}
+{%
+	enhanced,
+	breakable,
+	colback = mytheorembg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mytheoremfr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mytheoremfr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mytheoremfr},
+}
+{th}
+
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcolorbox{Theoremcon}
+{%
+	enhanced
+	,breakable
+	,colback = mytheorembg
+	,frame hidden
+	,boxrule = 0sp
+	,borderline west = {2pt}{0pt}{mytheoremfr}
+	,sharp corners
+	,description font = \mdseries
+	,separator sign none
+}
+
+
+%================================
+% Corollery
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{Corollary}{\corollarytitle}
+{%
+	enhanced
+	,breakable
+	,colback = myp!10
+	,frame hidden
+	,boxrule = 0sp
+	,borderline west = {2pt}{0pt}{myp!85!black}
+	,sharp corners
+	,detach title
+	,before upper = \tcbtitle\par\smallskip
+	,coltitle = myp!85!black
+	,fonttitle = \bfseries\sffamily
+	,description font = \mdseries
+	,separator sign none
+	,segmentation style={solid, myp!85!black}
+}
+{th}
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=chapter]{corollary}{\corollarytitle}
+{%
+	enhanced
+	,breakable
+	,colback = myp!10
+	,frame hidden
+	,boxrule = 0sp
+	,borderline west = {2pt}{0pt}{myp!85!black}
+	,sharp corners
+	,detach title
+	,before upper = \tcbtitle\par\smallskip
+	,coltitle = myp!85!black
+	,fonttitle = \bfseries\sffamily
+	,description font = \mdseries
+	,separator sign none
+	,segmentation style={solid, myp!85!black}
+}
+{th}
+
+
+%================================
+% LENMA
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{Lenma}{Lenma}
+{%
+	enhanced,
+	breakable,
+	colback = mylenmabg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mylenmafr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mylenmafr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mylenmafr},
+}
+{th}
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=chapter]{lenma}{Lenma}
+{%
+	enhanced,
+	breakable,
+	colback = mylenmabg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mylenmafr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mylenmafr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mylenmafr},
+}
+{th}
+
+
+%================================
+% PROPOSITION
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{Prop}{\proposaltitle}
+{%
+	enhanced,
+	breakable,
+	colback = mypropbg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mypropfr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mypropfr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mypropfr},
+}
+{th}
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=chapter]{prop}{\proposaltitle}
+{%
+	enhanced,
+	breakable,
+	colback = mypropbg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{mypropfr},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = mypropfr,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, mypropfr},
+}
+{th}
+
+
+%================================
+% CLAIM
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{claim}{\claimtitle}
+{%
+	enhanced
+	,breakable
+	,colback = myg!10
+	,frame hidden
+	,boxrule = 0sp
+	,borderline west = {2pt}{0pt}{myg}
+	,sharp corners
+	,detach title
+	,before upper = \tcbtitle\par\smallskip
+	,coltitle = myg!85!black
+	,fonttitle = \bfseries\sffamily
+	,description font = \mdseries
+	,separator sign none
+	,segmentation style={solid, myg!85!black}
+}
+{th}
+
+
+
+%================================
+% Exercise
+%================================
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=section]{Exercise}{\exercisetitle}
+{%
+	enhanced,
+	breakable,
+	colback = myexercisebg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{myexercisefg},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = myexercisefg,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, myexercisefg},
+}
+{th}
+
+\tcbuselibrary{theorems,skins,hooks}
+\newtcbtheorem[number within=chapter]{exercise}{\exercisetitle}
+{%
+	enhanced,
+	breakable,
+	colback = myexercisebg,
+	frame hidden,
+	boxrule = 0sp,
+	borderline west = {2pt}{0pt}{myexercisefg},
+	sharp corners,
+	detach title,
+	before upper = \tcbtitle\par\smallskip,
+	coltitle = myexercisefg,
+	fonttitle = \bfseries\sffamily,
+	description font = \mdseries,
+	separator sign none,
+	segmentation style={solid, myexercisefg},
+}
+{th}
+
+%================================
+% EXAMPLE BOX
+%================================
+
+\newtcbtheorem[number within=section]{Example}{\exampletitle}
+{%
+	colback = myexamplebg
+	,breakable
+	,colframe = myexamplefr
+	,coltitle = myexampleti
+	,boxrule = 1pt
+	,sharp corners
+	,detach title
+	,before upper=\tcbtitle\par\smallskip
+	,fonttitle = \bfseries
+	,description font = \mdseries
+	,separator sign none
+	,description delimiters parenthesis
+}
+{ex}
+
+\newtcbtheorem[number within=chapter]{example}{\exampletitle}
+{%
+	colback = myexamplebg
+	,breakable
+	,colframe = myexamplefr
+	,coltitle = myexampleti
+	,boxrule = 1pt
+	,sharp corners
+	,detach title
+	,before upper=\tcbtitle\par\smallskip
+	,fonttitle = \bfseries
+	,description font = \mdseries
+	,separator sign none
+	,description delimiters parenthesis
+}
+{ex}
+
+%================================
+% DEFINITION BOX
+%================================
+
+\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced,
+	before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
+	attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
+	boxed title style={frame code={
+					\path[fill=tcbcolback]
+					([yshift=-1mm,xshift=-1mm]frame.north west)
+					arc[start angle=0,end angle=180,radius=1mm]
+					([yshift=-1mm,xshift=1mm]frame.north east)
+					arc[start angle=180,end angle=0,radius=1mm];
+					\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
+						middle color=tcbcolback!80!black]
+					([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
+					[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
+					-- (frame.south east) -- (frame.south west)
+					-- ([xshift=-1mm,yshift=-1mm]frame.north west)
+					[sharp corners]-- cycle;
+				},interior engine=empty,
+		},
+	fonttitle=\bfseries,
+	title={#2},#1}{def}
+\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced,
+	before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
+	attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
+	boxed title style={frame code={
+					\path[fill=tcbcolback]
+					([yshift=-1mm,xshift=-1mm]frame.north west)
+					arc[start angle=0,end angle=180,radius=1mm]
+					([yshift=-1mm,xshift=1mm]frame.north east)
+					arc[start angle=180,end angle=0,radius=1mm];
+					\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
+						middle color=tcbcolback!80!black]
+					([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
+					[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
+					-- (frame.south east) -- (frame.south west)
+					-- ([xshift=-1mm,yshift=-1mm]frame.north west)
+					[sharp corners]-- cycle;
+				},interior engine=empty,
+		},
+	fonttitle=\bfseries,
+	title={#2},#1}{def}
+
+
+
+%================================
+% Solution BOX
+%================================
+
+\makeatletter
+\newtcbtheorem{question}{\questiontitle}{enhanced,
+	breakable,
+	colback=white,
+	colframe=myb!80!black,
+	attach boxed title to top left={yshift*=-\tcboxedtitleheight},
+	fonttitle=\bfseries,
+	title={#2},
+	boxed title size=title,
+	boxed title style={%
+			sharp corners,
+			rounded corners=northwest,
+			colback=tcbcolframe,
+			boxrule=0pt,
+		},
+	underlay boxed title={%
+			\path[fill=tcbcolframe] (title.south west)--(title.south east)
+			to[out=0, in=180] ([xshift=5mm]title.east)--
+			(title.center-|frame.east)
+			[rounded corners=\kvtcb@arc] |-
+			(frame.north) -| cycle;
+		},
+	#1
+}{def}
+\makeatother
+
+%================================
+% SOLUTION BOX
+%================================
+
+\makeatletter
+\newtcolorbox{solution}{enhanced,
+	breakable,
+	colback=white,
+	colframe=myg!80!black,
+	attach boxed title to top left={yshift*=-\tcboxedtitleheight},
+	title=Solution,
+	boxed title size=title,
+	boxed title style={%
+			sharp corners,
+			rounded corners=northwest,
+			colback=tcbcolframe,
+			boxrule=0pt,
+		},
+	underlay boxed title={%
+			\path[fill=tcbcolframe] (title.south west)--(title.south east)
+			to[out=0, in=180] ([xshift=5mm]title.east)--
+			(title.center-|frame.east)
+			[rounded corners=\kvtcb@arc] |-
+			(frame.north) -| cycle;
+		},
+}
+\makeatother
+
+%================================
+% Question BOX
+%================================
+
+\makeatletter
+\newtcbtheorem{qstion}{\questiontitle}{enhanced,
+	breakable,
+	colback=white,
+	colframe=mygr,
+	attach boxed title to top left={yshift*=-\tcboxedtitleheight},
+	fonttitle=\bfseries,
+	title={#2},
+	boxed title size=title,
+	boxed title style={%
+			sharp corners,
+			rounded corners=northwest,
+			colback=tcbcolframe,
+			boxrule=0pt,
+		},
+	underlay boxed title={%
+			\path[fill=tcbcolframe] (title.south west)--(title.south east)
+			to[out=0, in=180] ([xshift=5mm]title.east)--
+			(title.center-|frame.east)
+			[rounded corners=\kvtcb@arc] |-
+			(frame.north) -| cycle;
+		},
+	#1
+}{def}
+\makeatother
+
+\newtcbtheorem[number within=chapter]{wconc}{\wrongctitle}{
+	breakable,
+	enhanced,
+	colback=white,
+	colframe=myr,
+	arc=0pt,
+	outer arc=0pt,
+	fonttitle=\bfseries\sffamily\large,
+	colbacktitle=myr,
+	attach boxed title to top left={},
+	boxed title style={
+			enhanced,
+			skin=enhancedfirst jigsaw,
+			arc=3pt,
+			bottom=0pt,
+			interior style={fill=myr}
+		},
+	#1
+}{def}
+
+
+
+%================================
+% NOTE BOX
+%================================
+
+\usetikzlibrary{arrows,calc,shadows.blur}
+\tcbuselibrary{skins}
+\newtcolorbox{note}[1][]{%
+	enhanced jigsaw,
+	colback=gray!20!white,%
+	colframe=gray!80!black,
+	size=small,
+	boxrule=1pt,
+	title=\textbf{Bemerkung:-},
+	halign title=flush center,
+	coltitle=black,
+	breakable,
+	drop shadow=black!50!white,
+	attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2},
+	minipage boxed title=2.5cm,
+	boxed title style={%
+			colback=white,
+			size=fbox,
+			boxrule=1pt,
+			boxsep=2pt,
+			underlay={%
+					\coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$);
+					\coordinate (dotB) at ($(interior.east) + (0.5pt,0)$);
+					\begin{scope}
+						\clip (interior.north west) rectangle ([xshift=3ex]interior.east);
+						\filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east);
+					\end{scope}
+					\begin{scope}[gray!80!black]
+						\fill (dotA) circle (2pt);
+						\fill (dotB) circle (2pt);
+					\end{scope}
+				},
+		},
+	#1,
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% SELF MADE COMMANDS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}}
+\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}}
+\newcommand{\mlenma}[2]{\begin{Lenma}{#1}{}#2\end{Lenma}}
+\newcommand{\mprop}[2]{\begin{Prop}{#1}{}#2\end{Prop}}
+\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}}
+\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}}
+\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}}
+\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}}
+\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}}
+\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}}
+\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}}
+\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}}
+\newcommand{\nt}[1]{\begin{note}#1\end{note}}
+
+\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
+		Wrong Concept	\node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
+\newcommand\getcurrentref[1]{%
+	\ifnumequal{\value{#1}}{0}
+	{??}
+	{\the\value{#1}}%
+}
+\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}}
+\newenvironment{myproof}[1][\proofname]{%
+	\proof[\bfseries #1: ]%
+}{\endproof}
+
+\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}}
+\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{}
+
+\newcounter{mylabelcounter}
+
+\makeatletter
+\newcommand{\setword}[2]{%
+	\phantomsection
+	#1\def\@currentlabel{\unexpanded{#1}}\label{#2}%
+}
+\makeatother
+
+
+
+
+\tikzset{
+	symbol/.style={
+			draw=none,
+			every to/.append style={
+					edge node={node [sloped, allow upside down, auto=false]{$#1$}}}
+		}
+}
+
+
+% deliminators
+\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
+\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
+
+\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
+\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
+\DeclarePairedDelimiter{\round}{\lfloor}{\rceil}
+
+\newsavebox\diffdbox
+\newcommand{\slantedromand}{{\mathpalette\makesl{d}}}
+\newcommand{\makesl}[2]{%
+	\begingroup
+	\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}%
+	\pdfsave
+	\pdfsetmatrix{1 0 0.2 1}%
+	\rlap{\usebox{\diffdbox}}%
+	\pdfrestore
+	\hskip\wd\diffdbox
+	\endgroup
+}
+\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{%
+			\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}%
+		{\slantedromand\hspace{0.2ex}^{#1}}}}
+\ProvideDocumentCommand\dv{o m g}{%
+	\ensuremath{%
+		\IfValueTF{#3}{%
+			\IfNoValueTF{#1}{%
+				\frac{\dd #2}{\dd #3}%
+			}{%
+				\frac{\dd^{#1} #2}{\dd #3^{#1}}%
+			}%
+		}{%
+			\IfNoValueTF{#1}{%
+				\frac{\dd}{\dd #2}%
+			}{%
+				\frac{\dd^{#1}}{\dd #2^{#1}}%
+			}%
+		}%
+	}%
+}
+\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}}
+%  - others
+\DeclareMathOperator{\Lap}{\mathcal{L}}
+\DeclareMathOperator{\Var}{Var} % varience
+\DeclareMathOperator{\Cov}{Cov} % covarience
+\DeclareMathOperator{\E}{E} % expected
+
+% Since the amsthm package isn't loaded
+
+% I prefer the slanted \leq
+\let\oldleq\leq % save them in case they're every wanted
+\let\oldgeq\geq
+\renewcommand{\leq}{\leqslant}
+\renewcommand{\geq}{\geqslant}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% TABLE OF CONTENTS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\usepackage{tikz}
+\definecolor{doc}{RGB}{0,60,110}
+\usepackage{titletoc}
+\contentsmargin{0cm}
+\titlecontents{chapter}[3.7pc]
+{\addvspace{30pt}%
+	\begin{tikzpicture}[remember picture, overlay]%
+		\draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);%
+		\pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Kapitel \thecontentslabel};%
+	\end{tikzpicture}\color{doc!60}\large\sc\bfseries}%
+{}
+{}
+{\;\titlerule\;\large\sc\bfseries Seite \thecontentspage
+	\begin{tikzpicture}[remember picture, overlay]
+		\draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt);
+	\end{tikzpicture}}%
+\titlecontents{section}[3.7pc]
+{\addvspace{2pt}}
+{\contentslabel[\thecontentslabel]{2pc}}
+{}
+{\hfill\small \thecontentspage}
+[]
+\titlecontents*{subsection}[3.7pc]
+{\addvspace{-1pt}\small}
+{}
+{}
+{\ --- \small\thecontentspage}
+[ \textbullet\ ][]
+
+\makeatletter
+\renewcommand{\tableofcontents}{%
+	\chapter*{%
+	  \vspace*{-20\p@}%
+	  \begin{tikzpicture}[remember picture, overlay]%
+		  \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};%
+		  \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);%
+		  \clip (13,-.75) rectangle (20,1);
+		  \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};%
+	  \end{tikzpicture}}%
+	\@starttoc{toc}}
+\makeatother

fs25/mathematische_methoden/reihen_entwicklung.aux

@@ -0,0 +1,61 @@
+\relax 
+\providecommand{\transparent@use}[1]{}
+\providecommand\hyper@newdestlabel[2]{}
+\@setckpt{reihen_entwicklung}{
+\setcounter{page}{5}
+\setcounter{equation}{0}
+\setcounter{enumi}{0}
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+\setcounter{AlgoLine}{0}
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+\setcounter{algocfproc}{0}
+\setcounter{algocf}{0}
+\setcounter{AM@survey}{0}
+\setcounter{tcb@cnt@Theorem}{0}
+\setcounter{tcb@cnt@theorem}{0}
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+\setcounter{tcb@cnt@corollary}{0}
+\setcounter{tcb@cnt@Lenma}{0}
+\setcounter{tcb@cnt@lenma}{0}
+\setcounter{tcb@cnt@Prop}{0}
+\setcounter{tcb@cnt@prop}{0}
+\setcounter{tcb@cnt@claim}{0}
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+\setcounter{mylabelcounter}{0}
+\setcounter{lstlisting}{0}
+}

fs25/mathematische_methoden/taylor_laurentreihen/reihen_entwicklung.aux

@@ -0,0 +1,62 @@
+\relax 
+\providecommand{\transparent@use}[1]{}
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {section}{\numberline {3.1}Reihen-Entwichlung}{5}{section.3.1}\protected@file@percent }
+\@setckpt{taylor_laurentreihen/reihen_entwicklung}{
+\setcounter{page}{6}
+\setcounter{equation}{0}
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+}

fs25/mathematische_methoden/taylor_laurentreihen/reihen_entwicklung.tex

@@ -0,0 +1,3 @@
+\section{Reihen-Entwichlung}
+
+

fs25/mathematische_methoden/taylor_laurentreihen/taylor_laurentreihen.tex

@@ -0,0 +1,3 @@
+\chapter{Taylor- und Laurentreihen}
+
+\include{reihen_entwicklung.tex}

hs24/README.md

@@ -1,20 +0,0 @@
-# ITET 1. Semester (HS 2024)
-
-Im ersten Semester habe ich die folgenden Fächer belegt:
-
-- [Digitaltechnik](https://eth.jirayuruh.ch/hs24/digitech/)
-- [Lineare Algebra](https://eth.jirayuruh.ch/hs24/linalg/)
-- [Netzwerke und Schaltungen I](https://eth.jirayuruh.ch/hs24/nus/)
-- [Technische Mechanik](https://eth.jirayuruh.ch/hs24/techmech/)
-
-Weitere Information findet ihr im VZZ oder auf eurer Moodle Seite.
-
-## DISCLAIMER!!!
-
-Ich übernehme keine Haftung über mögliche Fehler in den Notizen (Es hat sicherlich ein paar drinnen, da ich teils Sätze umformuliert habe und meine Persönliche Notizen beigefügt habe!).
-
-Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden. Sie sind in der Fehlerliste ersichtlich.
-
----
-
-Made by JirR02 in Switzerland 🇨🇭

hs24/README.org

@@ -0,0 +1,26 @@
+#+title: ITET 1. Semester (HS 2024)
+
+#+author: JirR02
+Im ersten Semester habe ich die folgenden Fächer belegt:
+
+- [[https://eth.jirayuruh.ch/hs24/digitech/][Digitaltechnik]]
+- [[https://eth.jirayuruh.ch/hs24/linalg/][Lineare Algebra]]
+- [[https://eth.jirayuruh.ch/hs24/nus/][Netzwerke und Schaltungen I]]
+- [[https://eth.jirayuruh.ch/hs24/techmech/][Technische Mechanik]]
+
+Weitere Information findet ihr im VZZ oder auf eurer Moodle Seite.
+
+* DISCLAIMER!!!
+:PROPERTIES:
+:CUSTOM_ID: disclaimer
+:END:
+Ich übernehme keine Haftung über mögliche Fehler in den Notizen (Es hat
+sicherlich ein paar drinnen, da ich teils Sätze umformuliert habe und
+meine Persönliche Notizen beigefügt habe!).
+
+Fehler können per Discord, WhatsApp, Mail und Moodle gemeldet werden.
+Sie sind in der Fehlerliste ersichtlich.
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭