[Analysis] Add general notes

semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.tex

@@ -50,6 +50,7 @@
 
 
 \newpage
+\setcounter{section}{-1}
 \section{Introduction}
 This Cheat-Sheet does not serve as a replacement for solving exercises and getting familiar with the content.
 There is no guarantee that the content is 100\% accurate, so use at your own risk. 
@@ -68,12 +69,12 @@ And yes, she did really miss an opportunity there with the quote\dots But she wa
 This summary also uses tips and tricks from this \hlhref{https://polybox.ethz.ch/index.php/s/WBGFTRdEjRwJjQC}{Exercise Session}
 
 
-% TODO: Everywhere: Check with TA notes to add tips and tricks
-
 %          ╭────────────────────────────────────────────────╮
 %          │                    Content                     │
 %          ╰────────────────────────────────────────────────╯
 \newsection
+\input{parts/00_intro.tex}
+
 \section{Differential Equations}
 \input{parts/diffeq/00_intro.tex}
 \input{parts/diffeq/linear-ode/00_intro.tex}

semester3/analysis-ii/cheat-sheet-jh/parts/00_intro.tex

@@ -0,0 +1,3 @@
+\section{General tips}
+Use systems of equations if given some points, or other optimization techniques.
+The Analysis I cheat sheet has a derivatives and anti-derivatives table.

semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/04_green_formula.tex

@@ -11,7 +11,7 @@ with $\gamma_i = (\gamma_{i, 1}, \gamma_{i, 2}) : [a_i, b_i] \rightarrow \R^2$ a
 $f = (f_1, f_2)$ is a vector field of class $C^1$ on open set containing $X$. Then:
 \drmvspace
 \begin{align*}
-    \int_{X} \left( \frac{\partial f_2}{\partial x} - \frac{\partial f_1}{\partial_y} \right) \dx x \dx y = \sum_{i = 1}^{k} \int_{\gamma_i} f \cdot \dx \vec{s}
+    \int_{X} \left( \frac{\partial f_2}{\partial x} - \frac{\partial f_1}{\partial y} \right) \dx x \dx y = \sum_{i = 1}^{k} \int_{\gamma_i} f \cdot \dx \vec{s}
 \end{align*}
 
 \stepLabelNumber{all}\dhrmvspace
@@ -23,7 +23,7 @@ $\gamma_i$ as above, then
 \end{align*}
 
 \drmvspace
-\shade{gray}{Understanding and applying Green's Formula} The $\frac{\partial f_2}{\partial x} - \frac{\partial f_1}{y} = \text{curl}(f)$, i.e. it is the 2D-curl of $f$.
+\shade{gray}{Understanding and applying Green's Formula} The $\frac{\partial f_2}{\partial x} - \frac{\partial f_1}{\partial y} = \text{curl}(f)$, i.e. it is the 2D-curl of $f$.
 Thus, the sum of all line integrals is the same thing as the Riemann-Integral of the curl.
 
 We can use Green's Formula to compute integrals. For that we need the set of curves that define the set.