Comments
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I tried the following: a = 0 b = 2 n =25 1) The 24x24 matrix that approximates the 2nd derivative is $$U_{xx}=\begin{pmatrix} -312.5 & 156.25 & 0 & \ldots & 0 & 0 & 0\\ 156.25 & -312.5 & 156.25 & \ldots & 0 & 0 & 0\\ \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots\\ 0 & 0 & 0 &\ldots & 156.25 & -312.5 &…
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My matrix was: [0, 1, 3, 1, 2], [2, 0, 1, 3, 1], [2, 4, 0, 1, 3], [2, 3, 1, 0, 1], [4, 2, 2, 2, 0] My ranking was: Team 3: rating = 0.5273129974036033 Team 5: rating = 0.5215157378625016 Team 1: rating = 0.4172591286356548 Team 4: rating = 0.3713873702087703 Team 2: rating = 0.3713873702087703
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The steady-state temperature of the bar at the lower right corner is approximately $0.909$ [temperature units]
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Given the boundary and initial conditions, $u(t=1s) \approx 0.92$ [temperature units] at the midpoint of the insulated boundary.
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Bird face just looks ominous (。_。)
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by: $$g(x) = 4x^2 - 3x$$ At time $t=0$, its left end is set to temperature $0$ and its right end to $-1$. Sketch the temperature distribution at times: $$t=0, \: t=0.01, \: t=0.1, \text{ and } t=10$$
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Heat flow with a constant internal heat source is governed by the following model: $$u_t = 4u_{xx} + 5$$ Find the steady-state temperature distribution $u(x,t)$ if the boundary conditions are: $$u( 0, t) = -2; u( 1, t) = 4$$ Steady-state implies that nothing changes with time, therefore: $$\frac{du}{dt} = 0$$ Plugging the…
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$g(x)$ is the initial temperature distribution of the bar. It tells you the temperature at each point when $t = 0$. In other words, it represents $u(x,0)$. I want to say that a qualitative graph should suffice, but I'm not 100% sure. @mark could you weigh in on this one? edit: nvm, the times are too specific for this to be…
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Just testing $e^{i\pi}+1=0$
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The vertical displacement of the midpoint from equilibrium at time t = 1.6 [seconds] is approximately equal to -0.16 [unit lengths(?)].