sec-2: rewrite FWHM notes and add the relative image

slides/sections/2.md

@@ -55,14 +55,16 @@
 ## Landau median
 
 - CDF computed by numerical integration
-- QDF computed by numerical root-finding
+- Mean computed by numerical root-finding
+$$
+  F(x) = \frac{1}{2} \thus m_L\ex = 1.3557804...
+$$
 
 \setbeamercovered{}
 \begin{center}
-  \begin{tikzpicture}[remember picture]
-    \node at (0,0) (here) {$m_L\ex = 1.3557804...$};
+  \begin{tikzpicture}[overlay]
     \pause
-    \node [opacity=0.5, xscale=0.35, yscale=0.25 ] at (here) {\includegraphics{images/high.png}};
+    \node [opacity=0.5, xscale=0.35, yscale=0.25 ] at (2.4,0.95) {\includegraphics{images/high.png}};
   \end{tikzpicture}
 \end{center}
 
@@ -83,7 +85,8 @@
   \begin{tikzpicture}[remember picture]
     \node at (0,0) (here) {$\mu_L\ex = − 0.22278...$};
     \pause
-    \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here) {\includegraphics{images/high.png}};
+    \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here)
+          {\includegraphics{images/high.png}};
   \end{tikzpicture}
 \end{center}
 
@@ -92,27 +95,38 @@
 
 ## Landau FWHM
 
-We need to compute the maximum:
+::::: {.columns}
 
-$$
-  L_{\text{max}} = L(\mu_L)
-$$
-$$
-  \text{FWHM} = w = x_+ - x_- \with L(x_{\pm}) = \frac{L_{\text{max}}}{2}
-$$
+:::: {.column width=50%}
+  $$
+    \text{FWHM} = w = x_+ - x_-
+  $$
+  $$
+    L(x_{\pm}) = \frac{L_{\text{max}}}{2} = \frac{L(\mu_L)}{2}
+  $$
 
-. . .
+  . . .
 
-- Computed by numerical root finding (Brent)
+  \vspace{20pt}
 
-\setbeamercovered{}
+  - Computed by numerical root finding (Brent)
 
-\begin{center}
+  \setbeamercovered{}
+
+  \begin{center}
     \begin{tikzpicture}[remember picture]
-    \node at (0,0) (here) {$w_L\ex = 4.018645...$};
+      \node at (-1,0) (here) {$w_L\ex = 4.018645...$};
       \pause
-    \node [opacity=0.5, xscale=0.32, yscale=0.25 ] at (here) {\includegraphics{images/high.png}};
+      \node [opacity=0.5, xscale=0.65, yscale=0.5 ] at (here)
+            {\includegraphics{images/high.png}};
     \end{tikzpicture}
-\end{center}
+  \end{center}
 
-\setbeamercovered{transparent}
+  \setbeamercovered{transparent}
+::::
+
+::: {.column width=50%}
+  ![](images/fwhm.pdf)
+:::
+
+:::::