clarified grad curl div

shapeOfThingsToCome/digInGradCurlDiv.tex

@@ -306,14 +306,16 @@ \section{The shape of things to come}
   \begin{tikzpicture}
     \node{
       \begin{tikzcd}[ampersand replacement=\&, row sep=tiny, column sep=-5ex]
-        \& \& \& C^{\infty}(\R,\R^{\mathbf{1}}) \arrow[rr,"\ddx"] \& \& C^{\infty}(\R,\R^{\mathbf{1}}) \& \& \&  \\
-        \& \& C^{\infty}(\R^2,\R^{\mathbf{1}}) \arrow[rr,"\grad"] \& \& C^{\infty}(\R^2,\R^{\mathbf{2}}) \arrow[rr,"\curl"] \& \& C^{\infty}(\R^2,\R^{\mathbf{1}}) \& \&\\
-        \& C^{\infty}(\R^3,\R^{\mathbf{1}}) \arrow[rr,"\grad"] \& \& C^{\infty}(\R^3,\R^{\mathbf{3}}) \arrow[rr,"\curl"] \& \& C^{\infty}(\R^3,\R^{\mathbf{3}}) \arrow[rr,"\divergence"] \& \& C^{\infty}(\R^3,\R^{\mathbf{1}}) \& \\
+        \& \& \& C^{\infty}(\R,\R^{{1}}) \arrow[rr,"\ddx"] \& \& C^{\infty}(\R,\R^{{1}}) \& \& \&  \\
+        \& \& C^{\infty}(\R^2,\R^{{1}}) \arrow[rr,"\grad"] \& \& C^{\infty}(\R^2,\R^{{2}}) \arrow[rr,"\curl"] \& \& C^{\infty}(\R^2,\R^{{1}}) \& \&\\
+        \& C^{\infty}(\R^3,\R^{{1}}) \arrow[rr,"\grad"] \& \& C^{\infty}(\R^3,\R^{{3}}) \arrow[rr,"\curl"] \& \& C^{\infty}(\R^3,\R^{{3}}) \arrow[rr,"\divergence"] \& \& C^{\infty}(\R^3,\R^{{1}}) \& \\
         C^\infty(\R^4,\R) \arrow[rr] \&  \& C^\infty(\R^4,\R^4) \arrow[rr] \&  \& C^\infty(\R^4,\R^6) \arrow[rr] \&  \& C^\infty(\R^4,\R^4) \arrow[rr] \&  \& C^\infty(\R^4,\R) 
     \end{tikzcd}};
   \end{tikzpicture}
 \end{image}
-In the fourth row, four(!) fundamental theorems of calculus. This triangle can be extended \textit{infinitely!} Math folks who know this, eventually start calling all of these fundamental theorems ``\link[Stokes' Theorem]{https://en.wikipedia.org/wiki/Stokes_theorem}.'' Alas, our course has come to an end. However, it is really much more of a beginning, as there is so much more to know. 
+In the fourth row, there are four(!) fundamental theorems of calculus. Moreover, this triangle can be extended \textit{infinitely!} The details of this are beyond the scope of this course. Math folks who know this eventually start calling all of these fundamental theorems ``\link[Stokes' Theorem]{https://en.wikipedia.org/wiki/Stokes_theorem}.''
+
+Alas, our course has come to an end. However, it is really much more of a \textbf{beginning,} as there is \textbf{so much more to know.}