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Chapter  11 Fourier Series Chapter  11 Fourier Series

Chapter 11 Fourier Series - PowerPoint Presentation

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Chapter 11 Fourier Series - PPT Presentation

Chapter 11 Fourier Series 2 3 FIGURE 1121 Piecewisecontinuous function f in Example 1 4 FIGURE 1122 Piecewisecontinuous derivative f in Example 2 5 FIGURE 1123 Periodic extension of function ID: 772287

graph function odd problem function graph problem odd series fourier periodic partial reflection sums continuous respect symmetric piecewise figure

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Chapter 11 Fourier Series

2

3FIGURE 11.2.1 Piecewise-continuous function f in Example 1

4FIGURE 11.2.2 Piecewise-continuous derivative f ’ in Example 2

5FIGURE 11.2.3 Periodic extension of function f shown in Figure 11.2.1

6FIGURE 11.2.4 Partial sums of Fourier series (13) in Example 1

7FIGURE 11.3.1 Even function; graph symmetric with respect to y -axis

8FIGURE 11.3.2 Odd function; graph symmetric with respect to origin

9FIGURE 11.3.3 Odd function in Example 1

10FIGURE 11.3.4 Periodic extension of function shown in Figure 11.3.3

11FIGURE 11.3.5 Odd function in Example 2

12FIGURE 11.3.6 Partial sums of sine series (7)

13FIGURE 11.3.7 Even reflection

14FIGURE 11.3.8 Odd reflection

15FIGURE 11.3.9 Identity reflection

16FIGURE 11.3.10 Function f in Example 3 is neither odd nor even.

17FIGURE 11.3.11 Same function on (0, L ) but different periodic extensions

18FIGURE 11.3.12 Periodic forcing function for spring/mass system in Example 4

19FIGURE 11.3.13 Graph for Problem 39

20FIGURE 11.3.14 Graph for Problem 40

21FIGURE 11.3.15 Graph for Problem 41

22FIGURE 11.3.16 Graph for Problem 42

23FIGURE 11.3.17 Graph for Problem 50

24FIGURE 11.4.1 Positive roots x 1 , x 2 , x 3 , . . . of tan x = − x in Example 2

25FIGURE 11.5.1 Graphs of two partial sums of the Fourier-Bessel series in Example 2

26FIGURE 11.5.2 Partial sum S 5 ( x ) of the Fourier-Legendre series in Example 3

27FIGURE 11.R.1 Graph for Problem 18