I believe on section 2.6, example 1 there is a mis-referencing of equation (4) (D'Alembert's) in place of equation (5) (General Solution to wave equation). In Example 1, it says:

"Plugging (4) we see that $$\phi(ct)+\psi(−ct)=p(t)$$ as $$t>0, t>0 $$", (4) referring to D'Alembert's formula. However, I believe it results from plugging $$p(t)$$ into (5), the general solution $$u(x,t)=\phi(x+ct)+\psi(x−ct)$$

Again, later, it says:

"Then plugging $$x:=x+ct$$ into (6) and $$x:=x−ct$$ into (9) and adding we get from (4) that $$\begin{multline}

u(x,t)=

\underbracket{\frac{1}{2}g(x+ct)+

\frac{1}{2c}\int_0^{x+ct}h(x')\,dx'}_{=\phi(x+ct)}+ \\

\underbracket{p(t-x/c)-\frac{1}{2}g(ct-x)

-\frac{1}{2c}\int_0^{ct-x} h(x')\,dx'}_{=\psi(x-ct)}. \qquad

\end{multline}$$

Again, I believe this results from plugging the results into (5) and not (4).

I apologize if this correction seems a bit trivial but I personally had a bit of difficulty understanding where the results came from. Or maybe I am wrong and am missing something.