Differential Equations › Section H · Boundary value problems and Fourier series › Topic H.1
Boundary value problems
A guitar string is pinned at both ends and a metal rod has a temperature set at each end, so the conditions arrive at two different places rather than one starting point. Problems like these behave very differently from initial value problems, and that difference is the doorway to Fourier series.
In this topic
- Conditions at two places
- Kinds of boundary conditions
- Homogeneous boundary value problems
- Worked example: exactly one solution
- Same equation, new boundary
- Why uniqueness can fail
- Worked example: slope conditions
- Worked example: a forced equation
- Homogeneous problems: trivial or not
- An applied problem: a rod at steady state
- Common mistakes to avoid
- Key takeaways
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