12.1 Orthogonal Functions

12.2 Fourier Series

12.3 Fourier Cosine and Sine Series

12.4 Complex Fourier Series

12.5 Sturm–Liouville Problem

12.6 Bessel and Legendre Series

Chapter 12 in Review

In calculus you saw that a sufficiently differentiable function f could be expanded in a Taylor series, which is essentially an infinite series consisting of powers of x. The principal concept examined in this chapter also involves expanding a function in an infinite series. In the early 1800s, mathematicians developed the idea of expanding a function in a series of trigonometric functions. This idea is the linchpin of the procedures discussed in the two chapters that follow.