Differential Equations › Section H · Boundary value problems and Fourier series › Topic H.4
Fourier sine series
The eigenfunctions of a problem with both ends fixed are sines, so it is natural to ask whether an arbitrary function on an interval can be built from them. It can, and orthogonality hands us every coefficient with one integral.
In this topic
- Why build functions from sines
- The coefficient formula
- Odd functions and the odd extension
- Worked example: a constant
- Worked example: a parabola
- Worked example: a ramp
- How fast the coefficients shrink
- Applied example: a cooling rod
- Common mistakes to avoid
- Key takeaways
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