Fourier Series - Engineering Mathematics

In this slide fourier series of Engineering Mathematics has been described. one Example is also added for you. Hope this will help you understand fourier series.

1. Engineering Mathematics Presentation

2. Welcome to our Presentation Topic : “ FOURIER SERIES”

3. INDEX Definition. Conditions. Formula. Example. Conclusion.

4. DEFINITION FOURIER SERIES : Fourier Series is an infinite series representation of periodic function in terms of the trigonometric sine and cosine functions . Most of the single valued functions which occur in applied mathematics can be expressed in the form of Fourier series, which is in terms of sines and cosines .

5. DEFINITION Fourier series is to be expressed in terms of periodic functions- sines and cosines . Fourier series is a very powerful method to solve ordinary and partial differential equations, particularly with periodic functions appearing as non-homogeneous terms.

6. CONDITONS Let F(x) satisfy the following conditions : 1. F(x) is defined in the interval, c < x < c+2l. 2. F(x) and F’(x) sectionally continuous in c < x < c+2l. 3. F(x+2l) = F(x) i.e. F(x) is periodic with period 2l. If these 3 conditions remains, then we can say F(x) is Fourier series.

7. FORMULA The formula for a Fourier series on an  interval  [ , ] is : Where, And “𝑙” defines period, if period is specified then, period = 2 and if it is not then, the maximum limit will be the value of “𝑙” .  

8. FORMULA To do this math we need a shortcut formula, because we have trigonometric term in this formula. And we know that trigonometric term never ends.so we have to use this shortcut formula-  

9. EXAMPLE Expand F(x) = ; 0<x<2 and period = 2 Here, period = 2 or, 2 = 2 or, = Now,  

10. EXAMPLE  

11. EXAMPLE So. The Fourier series is : ( Answer :)  

12. Conclusion Conclusions To continue researching Fourier Series there are a few areas and specific problems that we would address . Fourier is a lengthy math, So we have to be careful about the formula while doing this math.

13. Thank you all for having patience.