This shows you the differences between two versions of the page.
Next revision | Previous revision Next revision Both sides next revision | ||
vpde_errata [2020/03/04 09:18] trinh created |
vpde_errata [2020/04/04 21:29] trinh |
||
---|---|---|---|
Line 1: | Line 1: | ||
====== Errata for the 2019-20' | ====== Errata for the 2019-20' | ||
- | ===== Typed notes ===== | + | ==== Typed notes ==== |
- | * The Corollary 8.4 on convex sets should specify that "if every **non-trivial | + | * The Corollary 8.4 on convex sets should specify that "if every straight line (**that includes a point on the interior of $\Omega$**) intersects $\partial\Omega$ at two points at most". |
+ | * There were some typos in the derivation of the wave equation in Chap. 10. It should instead look like this: | ||
+ | |||
+ | {{ :: | ||
+ | |||
+ | * Chap. 12 and the Definition 12.8 of the even extension on p.56 should read $x\in[0, L]$ instead of $x\in[0, \pi]$ | ||
+ | * Example 15.4 should read $0 < x < \pi$ instead of $0 < x < 2$. //(Courtesy DH)// | ||
+ | * Eqn (16.7) should have $\lambda^2$ instead of $\lambda$ on the equation for $G$. //(Courtesy DH)// | ||
+ | * Theorem 18.3 should read the initial conditions of $u(x, 0) = f(x)$ and $u_t(x, 0) = g(x)$. //(Courtesy RA)// | ||
+ | |||
+ | ==== Problem sets ==== | ||
+ | * PS5: Q1 should define the thermal conductivity as k not kappa. | ||
==== Solutions ==== | ==== Solutions ==== | ||
* PS3: Bottom of the first page $\partial \phi$ should be $\nabla \phi$ | * PS3: Bottom of the first page $\partial \phi$ should be $\nabla \phi$ | ||
+ | * PS3: Index notation needs to be removed from the main solutions in 19-20' delivery since the topic has been moved to the Appendix. Students are still free to use the technique if they learn it (as noted in lectures). | ||
* PS4 Q4 $dx$ and $dy$ transposed | * PS4 Q4 $dx$ and $dy$ transposed | ||
+ | * PS6 Q1. The function $\sin(x)\exp(-\cos(x^2))$ is indeed not periodic but not for the reasons stated in the solutions. The point here is that $\cos(x^2)$ is not a periodic function. You can verify this either by checking whether it's possible that $(x+L)^2 = x^2 + n*\pi$ independent of $x$, or simply by plotting the $\cos($x^2)$ and observing its behaviour, particularly near the origin. | ||
+ | ==== Lectures ==== | ||
+ | * Correction to {{ : |