[Analysis] Small notes

semester3/analysis-ii/cheat-sheet-rb/parts/05_diff.tex

@@ -295,12 +295,16 @@ $$
 Don't \textit{have to} exist if $X$ is open, only if $X$ is compact.\\
 \subtext{However, for compact sets, the lemma above no longer applies.}
 
-\method \textbf{Critical points on Compact Sets}\\
-Decompose $X = X' \cup B$, s.t. $X'$ is open, $B$ is a \textit{boundary}. 
+\method \textbf{Critical points on Compact Sets}
+
+\footnotesize
+Decompose $X = X' \cup B$, s.t. $X'$ (Interior) is open, $B$ is a \textit{boundary}. 
 \begin{enumerate}
-    \item Find critical points in $X'$
-    \item Check if any $x \in B$ is a maximum/minimum 
+    \item Find critical points in $X'$: via $\nabla f$, check state using $\textbf{H}_f$
+    \item Check if any $x \in B$ is a maximum/minimum\\
+    For this: try to parametrize (sections of) $B$, check corners.
 \end{enumerate}
+\normalsize
 
 \definition \textbf{Non-degenerate Critical Point}
 $$