From 1f10ac420b49ab95e558aa0477859f63a23b40b2 Mon Sep 17 00:00:00 2001
From: Raphael Kruse <65403623+rk-mlu@users.noreply.github.com>
Date: Sun, 2 Mar 2025 22:31:42 +0100
Subject: [PATCH] fixes a typo in chapter1

fixes #3
---
 book_src/chapters/chapter1.do.txt | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/book_src/chapters/chapter1.do.txt b/book_src/chapters/chapter1.do.txt
index 3729df8..87bcccb 100644
--- a/book_src/chapters/chapter1.do.txt
+++ b/book_src/chapters/chapter1.do.txt
@@ -55,7 +55,7 @@ in this book are initial value problems. As an example, consider the very simple
 \[ u'=u .\]
 !et
 This equation has the general solution $u(t)=Ce^t$ for any constant $C$, so it has an infinite number of solutions.
-Specifying an initial condition $u(t_0)=u_0$ gives $C=u_0$, and we get the unique solution $u(t)=u_0e^t$.  
+Specifying an initial condition $u(0)=u_0$ at time $t_0 = 0$ gives $C=u_0$, and we get the unique solution $u(t)=u_0e^t$.  
 We shall see that, when solving the equation numerically, we need to define $u_0$ in order to start our method and
 compute a solution at all.