[Analysis] Final tweaks

semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/00_line_integrals.tex

@@ -43,6 +43,7 @@ If any two points of $X$ can be joined by a parametrized curve, then $g$ is uniq
 \shortremark Two points $x, y \in X$ can be joined by parametrized curve $\gamma$ if $\gamma(a) = x$ and $\gamma(b) = y$. In that case, $X$ is called \bi{path-connected}.
 It is true when $X$ is \textit{convex} (e.g. when $X$ is a disc or a product of intervals).
 If $f$ is a vector field on $X$, then $g$ is called a \bi{potential} for $f$ and it is not unique, since we can add a constant to $g$ without changing the gradient.\\
+\shade{gray}{Finding a potential} We want a $g$ s.t. $\nabla g = f$ for some conservative $f$, so we find an anti-derivative $g$ for which $\nabla g = f$\\
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 \stepLabelNumber{all}
 \shortproposition For a vectorfield to be conservative, a \textit{necessary condition} is that $\displaystyle\frac{\partial f_i}{\partial x_j} = \frac{\partial f_j}{x_i}$