1. Chapter 7 Infinite Series

2. 7.6 Expand a function into the sine series and cosine series 3 The Fourier series of a function of period 2l 1 The Fourier series of odd function and even function 2 Expand a function into the sine or cosine series

3. 1 The Fourier series of odd function and even function Theorem 1 The Fourier coefficients for an even or odd function have special forms

4. Proof odd function even function

5. Similarly, we can prove (2) Example 1 Solution

6. picture of sum function

9. Periodic Extensions 2 Expand a function into the sine or cosine series Odd Extensions

10. Even Extensions

11. Example 2 Solution (1) Find sine series

13. (2) Find cosine series

15. 3 The Fourier series of a function of period 2l Theorem 2

16. Remark:

17. Example 3 Solution

18. Example 4 Solution

19. Example 5 Solution

22. or