Trinh @ Bath

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vpde_errata [2020/04/09 09:09]
trinh [Solutions] 		vpde_errata [2020/04/30 20:43]
trinh
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   * 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.   * 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 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...") there is a extra d/dt that should not be there.
  
 ==== Lectures ==== ==== Lectures ====
   * Correction to {{ :ma20223:ma20223-Week6.pdf |lectures 16}} when I wrote "Is $\exp(\cos x)$ periodic? (No)". Oops. It is periodic. Note that $\exp(f(x+L)) = \exp(f(x))$. A similar gaff appears in the solutions of PS6.    * Correction to {{ :ma20223:ma20223-Week6.pdf |lectures 16}} when I wrote "Is $\exp(\cos x)$ periodic? (No)". Oops. It is periodic. Note that $\exp(f(x+L)) = \exp(f(x))$. A similar gaff appears in the solutions of PS6. 
 +
 +==== Past exams ====
 +  * 2017-18 exam Q4d. The index should start from $n = 1$ once the $2n+1$ shift is done.
Last modified: 2020/04/30 20:43