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4 cards from this section. Quick, good the night before a test.
What is an initial condition in a PDE?
Think about what information you need at time t = 0.
Name the three types of boundary conditions.
Recall the DNR acronym.
What do Dirichlet conditions specify?
Recall the type of condition that dictates what is happening right at the edge.
True or False: A well-posed problem is one that is stable.
Consider what well-posed means in connection with solutions.
A cylindrical rod of length L is held at fixed temperatures at both ends (Dirichlet conditions). The initial temperature distribution is given as u(x,0) = sin(πx/L). Solve the PDE for different times t > 0.
Consider using Fourier series to express the initial condition.
A string fixed at both ends vibrates according to the wave equation with initial displacement u(x,0) = f(x) and initial velocity ∂u/∂t (x,0) = g(x). Derive the general solution of the wave equation subject to Neumann boundary conditions.
Focus on how the wave behavior is altered based on the boundary at the fixed ends.
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