### Author Topic: Section 2.6 errors  (Read 402 times)

#### Bruce Wu

• APM346X
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##### Section 2.6 errors
« on: October 11, 2015, 03:34:15 PM »
In text: http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.6.html#mjx-eqn-eq-2.6.23
The middle of paragraph b. it should be $u_{x}|_{x=b}=q_{r}(t)$ instead of $u_{x}|_{x=a}=q_{r}(t)$

In problem 2 part a.: http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.6.P.html#problem-2.6.P.2
At the bottom it is missing some letters. The different regions should be $x>c_{1}t,0<x<c_{1}t,-c_{2}t<x<0$ and $x<-c_{2}t$

#### Zaihao Zhou

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##### 2.6 errors
« Reply #1 on: October 15, 2015, 11:15:42 AM »
In 2.6 Example 1 equation $$\psi(x) = p(-x/c) - \phi(x)$$ is not correct, the correct one should be $$\psi(x) = p(-x/c) - \phi(-x)$$. OK

Also in the end of this example, statement " this formula defines u(x,t) as 0 < x < ct solution is given by (4)" does not flow. I think you meant "this formula defines u(x,t) as 0 < x < ct, recall for x>ct solution is given by (4)". OK

Also before example 5, equation (31)' seems should have been minus sign before the first integral, not a plus. also for the first term shouldn't it be 1/2(g(ct+x) minus  g(ct-x)) instead of plus?

NO, this is even continuation (for "primed") equations

For 1D wave equation on the finite interval, below the graph, section (b), ...(f.e...Ux|x=a =...) should be (f.e. Ux|x=b = ...).

No, intersection: as $u$ is defined where both $\phi(.)$ and $\psi(.)$ are