A thorough walkthrough of trigonometric Fourier series, covering derivation of coefficients via integration, convergence conditions (square-integrable, piecewise smooth functions), cosine and sine series for even/odd functions, periodic extensions of non-periodic functions, a worked triangular wave example, compact phase-shifted sinusoid form, complex Fourier series using Euler's formula, and the deep connection to linear algebra in Hilbert space where sinusoidal basis functions act as orthogonal vectors and Fourier coefficients are projections. Appendices cover key integral identities used throughout.
Table of contents
Coefficients of Fourier seriesConditions on f and convergence of Fourier seriesCosine and Sine seriesFourier series for a non-periodic function defined on an intervalExampleCompact formula using a single phase-shifted sinusoidComplex Fourier seriesFourier orthogonal basis in Hilbert spaceAppendix A: Integrals of sinusoidsAppendix B: Integrals of products of sinusoidsAppendix C: A useful integralAppendix D: Sinusoid with phase as a sum of sin and cos294 Impressions