From 85e7d741f78ca0874b42db5cfbd18f4c28a933b3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 2 Jun 2022 15:23:21 +0200
Subject: Add presentation

---
 .../laguerre/presentation/sections/laguerre.tex    | 88 ++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 buch/papers/laguerre/presentation/sections/laguerre.tex

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
new file mode 100644
index 0000000..cba9ffb
--- /dev/null
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -0,0 +1,88 @@
+\section{Laguerre-Polynome}
+
+\begin{frame}{Laguerre-Differentialgleichung}
+
+\begin{itemize}
+\item Benannt nach Edmond Nicolas Laguerre (1834-1886)
+\item Aus Artikel von 1879,
+in dem er $\int_0^\infty \exp(-x)/x \, dx$ analysierte
+\end{itemize}
+
+\begin{align*}
+x y''(x) + (1 - x) y'(x) + n y(x)
+ & =
+0
+, \quad
+n \in \mathbb{N}_0
+, \quad
+x \in \mathbb{R}
+\end{align*}
+
+\end{frame}
+
+\begin{frame}{Lösen der Differentialgleichung}
+
+\begin{align*}
+x y''(x) + (1 - x) y'(x) + n y(x)
+ & =
+0
+\\
+\end{align*}
+
+\uncover<2->{
+\centering
+\begin{tikzpicture}[remember picture,overlay]
+%% use here too
+\path[draw=mainColor, very thick,->](0, 1.1) to
+node[anchor=west]{Potenreihenansatz} (0, -0.8);
+\end{tikzpicture}
+}
+
+\begin{align*}
+\uncover<3->{
+L_n(x)
+ & =
+\sum_{k=0}^{n} \frac{(-1)^k}{k!} \binom{n}{k} x^k
+}
+\end{align*}
+\uncover<4->{
+\begin{itemize}
+    \item Die Lösungen der DGL sind die Laguerre-Polynome
+\end{itemize}
+}
+\end{frame}
+
+\begin{frame}
+\begin{figure}[h]
+\centering
+\scalebox{0.66}{\input{../images/laguerre_polynomes.pgf}}
+\caption{Laguerre-Polynome vom Grad $0$ bis $7$}
+\end{figure}
+\end{frame}
+
+\begin{frame}{Orthogonalität}
+\begin{itemize}[<+->]
+\item Beweis: Umformen in Sturm-Liouville-Problem (siehe Paper)
+\begin{alignat*}{5}
+((p(x) &y'(x)))' + q(x) &y(x) 
+&=
+\lambda &w(x) &y(x)
+\\
+((x e^{-x} &y'(x)))' + 0 &y(x)
+&=
+n &e^{-x} &y(x)
+\end{alignat*}
+\item Definitionsbereich $(0, \infty)$
+\item Gewichtsfunktion $w(x) = e^{-x}$
+\end{itemize}
+
+\only<4>{
+\begin{align*}
+\int_0^\infty e^{-x} L_n(x) L_m(x) \, dx
+=
+0
+,\quad
+n, m \in \mathbb{N}
+\end{align*}
+}
+\end{frame}
\ No newline at end of file
-- 
cgit v1.2.1


From fac45f54d4cee5018c063b4a720695cbf3040fa9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 2 Jun 2022 15:53:49 +0200
Subject: Correct typos in presentation

---
 buch/papers/laguerre/presentation/sections/laguerre.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index cba9ffb..faa50e5 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -34,7 +34,7 @@ x y''(x) + (1 - x) y'(x) + n y(x)
 \begin{tikzpicture}[remember picture,overlay]
 %% use here too
 \path[draw=mainColor, very thick,->](0, 1.1) to
-node[anchor=west]{Potenreihenansatz} (0, -0.8);
+node[anchor=west]{Potenzreihenansatz} (0, -0.8);
 \end{tikzpicture}
 }
 
@@ -76,7 +76,7 @@ n &e^{-x} &y(x)
 \item Gewichtsfunktion $w(x) = e^{-x}$
 \end{itemize}
 
-\only<4>{
+\uncover<4->{
 \begin{align*}
 \int_0^\infty e^{-x} L_n(x) L_m(x) \, dx
 =
-- 
cgit v1.2.1


From fb20b12bd912595deb6ad98a6428842f893edcda Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 2 Jun 2022 16:13:14 +0200
Subject: Add n != m to presentation at orthogonality section

---
 buch/papers/laguerre/presentation/sections/laguerre.tex | 2 ++
 1 file changed, 2 insertions(+)

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index faa50e5..1add511 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -81,6 +81,8 @@ n &e^{-x} &y(x)
 \int_0^\infty e^{-x} L_n(x) L_m(x) \, dx
 =
 0
+,\quad 
+n \neq m
 ,\quad
 n, m \in \mathbb{N}
 \end{align*}
-- 
cgit v1.2.1


From 8fb46098cb8e42a94b8e01ecc809f536d5c7efaf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Fri, 3 Jun 2022 07:23:21 +0200
Subject: Minor tweaks of presentation

---
 buch/papers/laguerre/presentation/sections/laguerre.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index 1add511..07cafb8 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -55,7 +55,7 @@ L_n(x)
 \begin{frame}
 \begin{figure}[h]
 \centering
-\scalebox{0.66}{\input{../images/laguerre_polynomes.pgf}}
+\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_polynomes.pgf}}
 \caption{Laguerre-Polynome vom Grad $0$ bis $7$}
 \end{figure}
 \end{frame}
-- 
cgit v1.2.1


From fde57297b3efbef28d09a532e1b3895d2b2ad917 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 14 Jul 2022 15:03:28 +0200
Subject: Correct Makefile, add text to gamma.tex, separate python-scripts for
 each image

---
 buch/papers/laguerre/presentation/sections/laguerre.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index 07cafb8..ed29387 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -55,7 +55,7 @@ L_n(x)
 \begin{frame}
 \begin{figure}[h]
 \centering
-\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_polynomes.pgf}}
+\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}}
 \caption{Laguerre-Polynome vom Grad $0$ bis $7$}
 \end{figure}
 \end{frame}
-- 
cgit v1.2.1


From e1f5d6267540ea8dc758696fb08cb7540362cf8f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Mon, 18 Jul 2022 17:34:37 +0200
Subject: First complete draft of Laguerre chapter

---
 buch/papers/laguerre/presentation/sections/laguerre.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

(limited to 'buch/papers/laguerre/presentation/sections/laguerre.tex')

diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index ed29387..f99214e 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -55,7 +55,8 @@ L_n(x)
 \begin{frame}
 \begin{figure}[h]
 \centering
-\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}}
+% \resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}}
+\includegraphics[width=0.7\textwidth]{../images/laguerre_poly.pdf}
 \caption{Laguerre-Polynome vom Grad $0$ bis $7$}
 \end{figure}
 \end{frame}
-- 
cgit v1.2.1

