Differential Equations › Section H · Boundary value problems and Fourier series › Topic H.2
Eigenvalues and eigenfunctions
A homogeneous boundary value problem usually has only the zero solution, but for certain special values of a parameter, nonzero solutions appear. Those values and solutions describe the notes a string can play, the loads at which a column buckles, and the building blocks of every Fourier series.
In this topic
- A parameter that decides everything
- Eigenvalues and eigenfunctions defined
- Three cases for lambda
- Worked example: both ends fixed
- Worked example: one end fixed, one end free
- Both ends insulated
- Periodic boundary conditions
- Sturm-Liouville problems
- Applied example: a buckling column
- Common mistakes to avoid
- Key takeaways
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