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4 cards from this section. Quick, good the night before a test.
Define eigenfunction in the context of PDEs.
Think about functions that remain unchanged apart from scaling.
What step follows after separating variables in a PDE?
Identify what your variables relate to.
What is the first step in the Eigenfunction Expansion Method?
Think about how we approach separating different parts.
True or False: Eigenvalues can be complex.
Recall the properties of eigenvalues in Sturm-Liouville problems.
Given the boundary conditions for a rod held at two ends and subjected to a heat flux, derive the eigenfunctions and eigenvalues. Next, use them to find the general solution of the heat equation.
Focus first on applying the correct boundary conditions to obtain eigenvalues.
Consider a wave equation defined on a string of length L with fixed ends. Describe how you would derive the first three eigenfunctions and show how they form a complete basis for the problem.
Use the knowledge of harmonic frequencies.
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