Experiments with Fourier Series

Part 5: Summary

1. For which functions of period 2 pi are the Fourier approximations composed entirely of cosine terms?
2. For which functions of period 2 pi are the Fourier approximations composed entirely of sine terms?
3. What features of the graph of a function indicate points at which the Fourier approximations are poorest?
4. What happens to the Fourier approximations of f at points of discontinuity of f?
5. Describe how we can use the convergence of Fourier approximations to find the exact sum of the series