taylorross

My matrix is:

matrix = [

  [0,3,4,1,3],

  [4,0,1,3,4],

  [4,3,0,4,4],

  [4,1,4,0,2],

  [2,4,3,4,0],

]

The ranking for my league is below. Team 3 is the highest ranked in the league.

Team 3: rating = 0.5176519293474793
Team 5: rating = 0.4613383888892107
Team 2: rating = 0.4237581736661745
Team 1: rating = 0.41451885767177027
Team 4: rating = 0.4096419141952378

The temperature in the lower right corner of the bar is $0.74727$.

The temperature near the midpoint of the insulated edge at $t=1 s$ is $2.18727$.

A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by

$$g(x) = 6x^2 - 2x.$$

At time $t=0$, its left end is set to temperature $3$ and its right end to $3$. Sketch the temperature distribution at times

$$t = 0, t = 0.01, t = 0.1, t = 10.$$

Heat flow with a constant internal heat source is governed by

$$u_t = 2u_{xx} + 8, u(0,t) = 1, u(1,t) = 7.$$

Find the steady state temperature distribution.

The steady state distribution is when $u_t = 0.$ I solved the given equation for $u_t = 0,$ which gives me the value of $u_{xx} = u''(x) = -4.$ I then antidifferentiated this expression twice to get a general solution for $u,$ and I plugged the boundary conditions into this general solution to get the steady state solution of $u(x) = -2x^2 + 8x + 1.$