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My matrix: [ [0,4,1,1,4], [1,0,1,2,3], [1,3,0,1,4], [2,3,1,0,1], [1,1,1,4,0] ] Eigenranking: Team 1: rating = 0.5312098699110835 Team 3: rating = 0.4855376577979557 Team 4: rating = 0.408991251670405 Team 5: rating = 0.39800103471102516 Team 2: rating = 0.39546250061814175 Team 1 is the best.
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The temperature at the lower right corner of the bar is $0.89869$.
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At $t = 1s$, the temperature near the midpoint of the insulating edge of the triangle is $0.29975$.
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x) = 3x^2 - 2x$$ At time $t = 0$ its left end is set to temperature 0 and its right end to 3. Sketch the temperature distribution at times: $t = 0,\ t = 0.01,\ t = 0.1,\ t = 10$ .
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Heat flow with a constant internal heat source is governed by $$u_t = 3u_{xx} + 4\ ; \ u(0,t) = 1, \ u(1,t) = 2$$ Find the steady state temperature distribution. Steady state: $u_t = 3u_{xx} + 4 = 0 \ \longrightarrow \ u_{xx} = -\frac{4}{3}$ $$u = \int\int -\frac{4}{3}\ dx = -\frac{2}{3}x^2 + c_{1}x + c_2$$ Initial…