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[PS] Start rewrite of max likelihood section

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Also adds various small quality of life improvements and simpler
explanations
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janishutz
2026-07-11 17:28:42 +02:00
parent d75e317fd4
commit 793401968b
19 changed files with 94 additions and 86 deletions
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semester4/ps/ps-jh/parts/10_tips-and-tricks/01_various.tex
+3
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@@ -55,3 +55,6 @@ $\cosh(x) := \frac{\sinh(x)}{\cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}} : \R
\subsubsection{Reihen}
\label{sec:series}
$\prod_{k = 1}^{n} \vartheta (1 - \vartheta)^{x_k - 1} = \vartheta^n (1 - \vartheta)^{S - n}$ mit $S = \sum_{k = 1}^{n} x_k$
% TODO: Add log and power laws
semester4/ps/ps-jh/parts/10_tips-and-tricks/02_diff-table.tex
+13 -11
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@@ -1,4 +1,6 @@
\newpage
\subsection{Tabelle von Auf- und Ableitungen}
Für Integrale von stückweisen Funktionen, stückweise Integrieren und aufsummieren.
\begin{scriptsize}
\begin{tables}{lll}{\tr{Antiderivative}{Stammfunktion} & \tr{Function}{Funktion} & \tr{Derivative}{Ableitung}}
$\displaystyle \frac{x^{n + 1}}{n + 1}$ & $x^n$ & $n \cdot x^{n - 1}$ \\
@@ -40,14 +42,14 @@
$\arcsin \left( \frac{x}{|a|} \right)$ & $\frac{1}{\sqrt{x^2 - a^2}}$ \\
$\frac{1}{a}\arctan \left( \frac{x}{|a|} \right)$ & $\frac{1}{a^2 - x^2}$ \\
\end{tables}
\begin{tables}{cc}{$F(x)$ & $f(x)$}
$-\frac{1}{a} \cos(ax + b)$ & $\sin(ax + b)$ \\
$\frac{1}{a} \sin(ax + b)$ & $\cos(ax + b)$ \\[1mm]
\hline
$x^x$ & $x^x \cdot (1 + \ln|x|)$ \\
$(x^x)^x$ & $(x^x)^x \cdot (x + 2x\ln|x|)$ \\
$x^{(x^x)}$ & $x^{(x^x)} \cdot (x^{x - 1} + \ln|x| \cdot x^x (1 + \ln|x|))$ \\
\hline \\[-3mm]
$\frac{1}{2}(x - \frac{1}{2} \sin(2x))$ & $\sin(x)^2$ \\[1mm]
$\frac{1}{2}(x + \frac{1}{2} \sin(2x))$ & $\cos(x)^2$ \\
\end{tables}
% \begin{tables}{cc}{$F(x)$ & $f(x)$}
% $-\frac{1}{a} \cos(ax + b)$ & $\sin(ax + b)$ \\
% $\frac{1}{a} \sin(ax + b)$ & $\cos(ax + b)$ \\[1mm]
% \hline
% $x^x$ & $x^x \cdot (1 + \ln|x|)$ \\
% $(x^x)^x$ & $(x^x)^x \cdot (x + 2x\ln|x|)$ \\
% $x^{(x^x)}$ & $x^{(x^x)} \cdot (x^{x - 1} + \ln|x| \cdot x^x (1 + \ln|x|))$ \\
% \hline \\[-3mm]
% $\frac{1}{2}(x - \frac{1}{2} \sin(2x))$ & $\sin(x)^2$ \\[1mm]
% $\frac{1}{2}(x + \frac{1}{2} \sin(2x))$ & $\cos(x)^2$ \\
% \end{tables}