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Fixes two minor issues in Chapter 1 #5

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Fixes two minor issues in Chapter 1 #5

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f5db0b5
Typo in class ForwardEuler_v0
rk-mlu Mar 2, 2025
86fd2dd
Fixes a sign error in Section 1.3
rk-mlu Mar 3, 2025
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6 changes: 3 additions & 3 deletions book_src/chapters/chapter1.do.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -309,7 +309,7 @@ class ForwardEuler_v0:
"""Compute solution for t_span[0] <= t <= t_span[1],
using N steps."""
t0, T = t_span
self.dt = T / N
self.dt = (T - t0) / N
self.t = np.zeros(N + 1) # N steps ~ N+1 time points
self.u = np.zeros(N + 1)

Expand Down Expand Up @@ -394,8 +394,8 @@ by systems of ODEs, i.e., multiple ODEs where the right-hand side of one equatio
systems are also referred to as vector ODEs. One simple example is
!bt
\begin{alignat*}{2}
u' &= v, \quad &&u(0) = 1\\
v' &= -u, \quad &&v(0) = 0.
u' &= -v, \quad &&u(0) = 1\\
v' &= u, \quad &&v(0) = 0.
\end{alignat*}
!et
The solution of this system is $u=\cos t, v=\sin t$, which can easily be verified by inserting the solution into the equations
Expand Down