[Analysis] Notes and cleanup

Notes for tangent space computation and green's formula.
Also includes fixes for the pagination as result of additions

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

@@ -27,7 +27,7 @@ $\gamma_i$ as above, then
 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.
-For the unit circle, that is just one curve,
+For the \bi{unit circle}, that is just one curve,
 being $\gamma(t) = \begin{pmatrix}
         R \cdot \cos(t) \\
         R \cdot \sin(t)
@@ -53,9 +53,8 @@ That set is derived from the image that is given for the line.
 Be cognizant of what direction the integral goes, if the set is on the right hand side of the curve, the final result has to be negated to change the direction of the integral.
 If the curve doesn't fully enclose the set, then we can simply compute the line integrals of the missing sections and subtract them from the final result.
 
-We can also use known formulas to compute the area of discs, etc (like $r^2 * \pi$ for a circle).
-To calculate the area enclosed by a curve using Green's formua, we can use the vector field
-% TODO: Finish
+We can also use known formulas to compute the area of discs, etc (like $r^2 \cdot \pi$ for a circle).
+To calculate the area enclosed by a curve using Green's formua, if not given a vector field, we can use the vector field $F(x, y) = (0, x)$.
 
 \shade{gray}{Center of mass}
 The center of mass of an object $\cU$ is given by $\displaystyle \overline{x}_i = \frac{1}{\text{Vol}(\cU)} \int_{\cU} x_i \dx x$.