Suppose we have a laterally insulated metal rod of length 2, parametrized by length, starting with 0 at the left hand endpoint. Suppose the left hand endpoint is kept at temperature -9, the right hand endpoint is kept at temperature 9, and the initial temperature at time t = 0 is sin(x). Set up the initial-boundary-value-problem (IBVP). The equation is: Ⓒutt=a²uzz Ⓒu₁ = a²urz + u Utt + Uzz = 0 Ⓒut=a²UTT Range of idependent variables: 0 < x < t> 0, Boundary and initial conditions: u (0,t) = u( u(x, 0) = help (formulas) ,t) = for t > 0, for t > 0,

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