From 38029c5e7958d6f8f58a797ab063efd75c5b314f Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Tue, 15 Sep 2020 22:07:50 +0200
Subject: [PATCH] fix math
---
src/8_differential_equations_2.md | 16 ++++++++--------
1 file changed, 8 insertions(+), 8 deletions(-)
diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index 3309480..b1034f9 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -56,11 +56,11 @@ $$y_{1} = y, \ y_{2} = y', \ \cdots, \ y_{n} = y^{(n-1)}.$$
Then, the differential equation can be re-written as
$$\begin{split}
-y_1 ' & = & y_2 \\
-y_2 ' & = & y_3 \\
-& \vdots & \\
-y_{n-1} '& = & y_{n} \\
-y_{n} ' & = & - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}.
+y_1 ' & = y_2 \\
+y_2 ' & = y_3 \\
+& \vdots \\
+y_{n-1} '& = y_{n} \\
+y_{n} ' & = - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}.
\end{split}$$
Notice that together these $n$ equations form a linear first order system, the
@@ -145,9 +145,9 @@ $$P(\lambda) = \lambda^n + a_{n-1} \lambda^{n-1} + \cdots + a_0.$$
+ a_0$$
$$- \det(A - \lambda I) = P(\lambda).$$
-In the second last line of the proof we indicated that the method of co-factor
-expansion demonstrated is repeated an additional $n-2$ times. This completes the
-proof.
+ In the second last line of the proof we indicated that the method of
+ co-factor expansion demonstrated is repeated an additional $n-2$ times.
+ This completes the proof.
With the characteristic polynomial, it is possible to write the differential
equation as
--
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