1. Mathematics 2 the First and Second Lectures
Third week
/ 5/ 1438هـ
أ / سمر السلمي

2. Outline for today Office Hours first homework due Chapter One
Fourier Series
Solving examples of Fourier Coefficients
Complex form of Fourier Series
Solving examples of Complex form of Fourier Series
Other Intervals
Even and Odd Functions

3. Office Hours Time of Periodic Exams
Sunday, Tuesday and Thursday from 11 to 12 p.m.
you can put any paper or homework in my mailbox in Faculty of Physics Department
I will put any announcement or apology in my website ( , so please check it
my is for any question.
every Wednesday a homework will be submit at my mailbox (or if you did not came to university )
every week a worksheet will be submit in class
Time of Periodic Exams
The first periodic exam in / 6 / 1438 h every in her group
The second periodic exam in / 8 / 1438 h every in her group

4. The Second Homework
I put the second homework in my website in the university at Friday
homework Due Wednesday 2 / 6 / 1438 هـ in my mailbox in Faculty of Physics Department
I will not accept any homework after that , but if you could not come to university you should sent it to me by in the same day than put the paper next day in my mailbox

5. Chapter One: Ch 7, pg. 297
Fourier Series
Fourier Coefficients
Section 5, pg 307 – 312
Complex form of Fourier Series
Section 7, pg 315 – 317
Other Intervals
Section 8, pg

6. Complex form of Fourier series
we can write the general formula for Fourier Series with the exponential form or complex form By replace exponential function with sine –cosine function
Thus
To find the value of coefficient c0
all the integrals on the right – hand side are zero except the first term (zero term), if we use the equation below :

7. Complex form of Fourier series
Continue finding the value of coefficient c0
all the integrals on the right – hand side are zero except the first term (zero term), then take the average value for all terms on the same interval (-π, π) :
Thus
thus

8. Complex form of Fourier series To find the value of coefficient cn
If we use the equation below :
all terms in right – hand will be zero except the nth term because k = (n-n) =0

9. Complex form of Fourier series
Continue finding the value of coefficient cn
all terms in right – hand will be zero except the nth term for sin nx if , then
thus
Because we now know the nth term for einx , we will know the other values
The same for zero term

10. Complex form of Fourier series
Solving Fourier Series’ problems
First, we find the value complex coefficients from 2 eq.
Second, we put them in The general complex formula for Fourier Series

11. Fourier Coefficients
Expand the periodic function f(x) in a complex exponentials from of Fourier Series 1)

12. Other intervals
we can replaced the interval (-π, π) to other intervals (0, 2π) , (-2π, 0) , (π, 3π) , (2π, 4π) , (-π, -3π) . (a , 2π + a) etc as long as the Length is 2π

13. Other intervals
We will change the from with different angle and interval from π to l
we can replaced the interval (-l, l) to other intervals (0, 2l) , (-2l, 0) , (l, 3l) , (2l, 4l) , (-l, -3l) . (a , 2l + a) etc as long as the Length is 2l

14. Expand the periodic function f(x) in a sine-cosine Fourier Series or in a complex exponentials ?

15. Expand the periodic function f(x) in a sine-cosine Fourier Series or in a complex exponentials ?
ao or co (Worksheet )

16. Next class review
Even and Odd Functions
An Applications to Sound