1. Mathematics 2 The eleventh and Twelfth Lectures
The seventh and eighth weeks
/ 6/ 1438 هـ
أ / سمر السلمي

2. Outline for today Office Hours fifth homework due
Chapter three : Special functions
Beta functions:
Beta functions in terms of the gamma Functions
Error function
Chapter Four :Differential Equations of The Special Functions
Legendre's Equation
Legendre Polynomials

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 second periodic exam in / 8 / 1438 h every in her group

4. The Fifth Homework
I put the fifth homework in my website in the university at Friday
homework Due Wednesday 15 / 7/ 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 11, pg. 457
Beta functions:
Section 6, pg
Beta functions in terms of the gamma Functions
Section 7, pg
Error functions:
Section 9, pg
Chapter Three: Ch 12, pg. 483
Legendre Equation & Polynomials
Section 2, pg pg 488

6. Beta Function
p > 0 , q > 0
prove
prove
prove

7. Beta Function
Some Relation
prove

8. Beta Function in terms of the gamma Function prove
Express the following integrals as Beta functions in terms of gamma functions ? then use gamma function's table in next slide
(worksheet)

10. Error Function
You can see it in probability theory in statistical mechanics
The error function is the area under part of this curve
Definition:

11. Error Function
The other related integrals which often referred to error function
a) The Normal or Gaussian distribution function
b) The complement error function

12. Error Function
We can use to write erf(x) in terms of Gaussian distribution and complementary error function
Some facts about error function prove ( 1 , 2 , 3 )
1- erf (x) is odd erf (-x) = - erf (x)
2- for large x x > 3
erf ( ∞ ) = 1
3- for small x I x I << 1

13. Find the value of error function?
the Error Function
Find the value of error function?
erf (0.7)
erf (0.003)

14. the Legender Functions
l constant
The general solution of the Legendre's differential equation ?

15. Next class review
Legender Functions