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| + | * 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)// | ||
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| + | ==== Problem sets ==== | ||
| + | * PS5: Q1 should define the thermal conductivity as k not kappa. | ||
| ==== Solutions ==== | ==== Solutions ==== | ||
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| * 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). | * 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. | ||
| + | * **PS9 Q2:** There is a missing factor of $p$ on the bottom here. See Lecture 29. | ||
| + | * **PS9 Q4:** Looks like axes were doubled here. //(Courtesy RA, HC)// | ||
| + | * **PS10 Q2:** Looks like there are a few $\kappa$s missing on the right hand side (I count three); **Q3** In the redefinition of the energy (above "So now you are back to..." | ||
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| + | ==== Lectures ==== | ||
| + | * Correction to {{ : | ||
| + | ==== Past exams ==== | ||
| + | * 2017-18 exam Q4d. The index should start from $n = 1$ once the $2n+1$ shift is done. | ||