Differential Equations › Section H · Boundary value problems and Fourier series › Topic H.7
Convergence of Fourier series
So far we have written an equals sign between a function and its Fourier series without asking whether the infinite sum really adds up to the function. This topic answers that: where the series converges to f, what it does at jumps, and when it may be differentiated term by term.
In this topic
- Does the series equal the function?
- Piecewise smooth functions
- The convergence theorem
- Worked example: the half ramp
- Worked example: a square wave
- Sine and cosine series
- The Gibbs phenomenon
- Term-by-term differentiation
- Worked example: differentiate or not?
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…