Chapter 11 Fourier Series

FIGURE 11.2.1 Piecewise-continuous function f in Example 1

FIGURE 11.2.2 Piecewise-continuous derivative f’ in Example 2

FIGURE 11.2.3 Periodic extension of function f shown in Figure 11.2.1

FIGURE 11.2.4 Partial sums of Fourier series (13) in Example 1

FIGURE 11.3.1 Even function; graph symmetric with respect to y-axis

FIGURE 11.3.2 Odd function; graph symmetric with respect to origin

FIGURE 11.3.3 Odd function in Example 1

FIGURE 11.3.4 Periodic extension of function shown in Figure 11.3.3

FIGURE 11.3.5 Odd function in Example 2

FIGURE 11.3.6 Partial sums of sine series (7)

FIGURE 11.3.7 Even reflection

FIGURE 11.3.8 Odd reflection

FIGURE 11.3.9 Identity reflection

FIGURE 11.3.10 Function f in Example 3 is neither odd nor even.

FIGURE 11.3.11 Same function on (0, L) but different periodic extensions

FIGURE 11.3.12 Periodic forcing function for spring/mass system in Example 4

FIGURE 11.3.13 Graph for Problem 39

FIGURE 11.3.14 Graph for Problem 40

FIGURE 11.3.15 Graph for Problem 41

FIGURE 11.3.16 Graph for Problem 42

FIGURE 11.3.17 Graph for Problem 50

FIGURE 11.4.1 Positive roots x1, x2, x3, . . . of tan x = −x in Example 2

FIGURE 11.5.1 Graphs of two partial sums of the Fourier-Bessel series in Example 2

FIGURE 11.5.2 Partial sum S5(x) of the Fourier-Legendre series in Example 3

FIGURE 11.R.1 Graph for Problem 18