1. Fourier Series: Examples

2. Factor: 1/
(1/2)Sin 2
Sin =

3. Sin +
(1/2)Sin 2

4. Sin
+ (1/2)Sin 2
+ (1/3)Sin 3
+ (1/4)Sin 4

5. 6 terms of the series

6. 10 terms of the series

7. 20 terms of the series

8. Factor: 4/
Sin
(1/3)Sin3

9. Sin +
(1/3)Sin3

10. Sin
+(1/3)Sin3
+(1/5)Sin5
+(1/7)Sin7

11. 6 terms of the series

12. 10 terms of the series

13. 20 terms of the series

14. Cos
+ (1/9)Cos 3
Factor: 8/ 2

15. Cos
+ (1/9)Cos 3
+ (1/25)Cos 5
+ (1/49)Cos 7

16. 8 terms of the series

17. Fourier Series:
f(t), t
<
< T
f(t) =A0 + A1 Cos A2 Cos 2
+ A3 Cos A4 Cos …….
+ B1 Sin B2 Sin B3 Sin …
f(t)
A0 =
f(t)
Cos n
An / 2 =

18. Orthogonality relations
Bm / 2 =
f(t)
Sin m
Cos n
Sin m
= 0
Cos n
Cos m
= 0
Sin n
Sin m
= 0
n and m
are different
Orthogonality relations