1. Introduction to the Theory of Fourier's Series and Integrals;Carslaw,1921
2. Fourier Series and Boundary Value Problems;Churchill,1993
3. Methods of Mathematical Physics;Jeffreys,1972
4. Fourier Series;Kufner,1971
5. Lanczos, C., Applied Analysis. Englewood Cliffs, NJ: Prentice-Hall (1956), reprinted, Dover (1988). The book gives a well-written presentation of the Lanczos convergence technique (which suppresses the Gibbs phenomenon oscillations). This and several other topics are presented from the point of view of a mathematician who wants useful numerical results and not just abstract existence theorems.