[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/diffeq/00_intro.tex

@@ -5,3 +5,5 @@ $f' - a = 0$ has only solution $f(x) = \int_{x_0}^{x} a(t) \dx t$
 \setcounter{all}{6}
 \shorttheorem Let $F: \R^2 \rightarrow \R$ be a differential function of two variables. Let $x_0 \in \R$ and $y_0 \in \R^2$.
 The Ordinary Differential Equation (ODE) $y' = F(x, y)$ has a unique solution $f$ defined on a ``largest'' interval $I$ that contains $x_0$ such that $y_0 = f(x_0)$
+
+A diffeq is ordinary if it has only one variable and is evaluated at the same point.

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

@@ -1,6 +1,6 @@
 \newsectionNoPB
 \subsection{Linear Differential Equations}
-An ODE is considered linear if and only if the $y$s are only scaled and not part of powers.\\
+An ODE is considered \bi{linear} if and only if the $y$s are only scaled and not part of powers.\\
 \compactdef{Linear differential equation of order $k$} (order = highest derivative)
 $y^{(k)} + a_{k - 1}y^{(k - 1)} + \ldots + a_1 y' + a_0 y = b$, with $a_i$ and $b$ functions in $x$.
 If $b(x) = 0 \smallhspace \forall x$, \bi{homogeneous}, else \bi{inhomogeneous}\\

semester3/analysis-ii/cheat-sheet-jh/parts/diffeq/linear-ode/02_constant-coefficient.tex

@@ -29,5 +29,5 @@ The homogeneous equation will then be all the elements of the set summed up.\\
     \item \bi{Separation of variables} For equations of form $y' = a(y) \cdot b(x)$ (Note: Not linear),
           we transform into $\frac{y'}{a(y)} = b(x)$ and then integrate by substituting $y'(x) dx = dy$, changing the variable of integration.
           Solution: $A(y) = B(x) + c$, with $A = \int \frac{1}{a}$ and $B(x) = \int b(x)$.
-          To get final solution, solve for the above equation for $y$.
+          To get final solution, solve the above equation for $y$.
 \end{itemize}