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.