align fix; theorem style; condition number

quarto/ODEs/euler.qmd

@@ -602,12 +602,13 @@ $$
 
 We can try the Euler method here. A simple approach might be this iteration scheme:
 
-
+$$
 \begin{align*}
 x_{n+1} &= x_n + h,\\
 u_{n+1} &= u_n + h v_n,\\
 v_{n+1} &= v_n - h \cdot g/l \cdot \sin(u_n).
 \end{align*}
+$$
 
 Here we need *two* initial conditions: one for the initial value $u(t_0)$ and the initial value of $u'(t_0)$. We have seen if we start at an angle $a$ and release the bob from rest, so $u'(0)=0$ we get a sinusoidal answer to the linearized model. What happens here? We let $a=1$, $l=5$ and $g=9.8$: