[Analysis] Clean up, add some notes

semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/00_continuity.tex

@@ -11,7 +11,6 @@ $(x_k)$ converges to $y$ as $k \rightarrow +\infty$ if $\forall \varepsilon > 0
 \bi{(1)} Let $x_0 \in X$. $f$ continuous in $\R^n$ if $\forall \varepsilon > 0 \smallhspace \exists \delta > 0$ s.t. if $x \in X$ satisfies $||x - x_0|| < \delta$,
 then $||f(x) - f(x_0)|| < \varepsilon$
 \bi{(2)} $f$ continuous \textit{on} $X$ if continuous at $x_0 \smallhspace \forall x_0 \in X$
-% TODO: Add tricks from TA slides here (week 05 / 04)
 % ────────────────────────────────────────────────────────────────────
 \shortproposition Let $X$ and $f$ as prev. Let $x_0 \in X$. $f$ continuous at $x_0$ iff $\forall (x_k)_{k \geq 1}$ in $X$ s.t.
 $x_k \rightarrow x_0$ as $k \rightarrow +\infty$, $(f(x_k))_{k \geq 1}$ in $\R^m$ converges to $f(x)$\\

semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/04_change_of_variable.tex

@@ -2,4 +2,3 @@
 \subsection{Change of variable}
 The idea is to substitute variables for others that make the equation easier to solve.
 A common example is to switch to polar coordinates from cartesian coordinates, as already demonstrated with continuity checks
-% TODO: Add notes from TA notes