1. Mathematics 2 the Seventh and Eighth Lectures
Fifth week
/ 6/ 1438هـ
أ / سمر السلمي

2. Outline for today Office Hours fourth homework due Chapter One
Fourier Transforms
Chapter Two
Dirac Delta Function

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 Fourth Homework
I put the fourth homework in my website in the university at Friday
homework Due Wednesday 16 / 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 Three: Ch 15, pg. 647
Integral Transforms
Fourier Transforms
Section 4, pg 647 – 654
(notice: in the 3rd ed it will be ch 7 Section 12)
The Dirac Delta Function
Section 7, pg 669 (notice: in the 3rd ed it will be ch 8 Section 11)
Also, (will take Dirac Delta Function from another book (Introduction to Electrodynamics by David Griffiths & Reed College Ch 1 Section 5.2,)
(this part will be as a PDF file in my website in Lectures

6. Definition of fourier transforms
The f(x) and g(α) a pair of fourier transforms
g(α) is called the fourier transforms of f(x)
f(x) is called the inverse fourier transforms of g(α)
Common simply to ca either a fourier transforms of the other

7. fourier sine transforms fourier cosine transforms
Fourier Transforms
fourier sine transforms
The fs(x) and gs(α) a pair of fourier sine transforms
Representing odd function
fourier cosine transforms
The fc(x) and gc(α) a pair of fourier cosine transforms
Representing even function

8. Fourier Transforms Let f(x) is a nonperiodic function ,
Find the exponential Fourier transform of f(x) and write f(x)as a Fourier integral ?
or the Fourier cosine transform of f(x) and write it as a Fourier integral ?

9. Fourier Transforms Let f(x) is a nonperiodic function ,
Find the exponential Fourier transform of f(x) and write f(x)as a Fourier integral ?
or the Fourier sine transform of f(x) and write it as a Fourier integral ?

10. Dirac Delta Function
can be pictured as an infinitely high infinitesimally narrow “spike” with area 1
is generalized f(x) or distribution

11. Dirac Delta Function
Example: Evaluate the following integral

12. Dirac Delta Function
Proof of the
At x=0 so

13. Dirac Delta Function
Proof of the
At x=a so

14. Dirac Delta Function Properties of delta function 1)
if delta function of 2)
k ≠ 0 3) 4)
a ≠ b

15. Dirac Delta Function Proof of the y=kx dy = k dx x = y / k
limit integer to for k is positive
limit integer to for k is negative
So it is true that

16. Dirac Delta Function
Proof of the
u=x
du = dx
= 0 -
So it is true that

17. Dirac Delta Function Fourier transform of a delta function
Inverse transforms

18. Dirac Delta Function Example: Evaluate the following integral
(Worksheet )

19. Next class review
Gamma Function
Beta Function