1. Mathematics 2 The thirteenth and fourteenth Lectures
The tenth week
/ 7/ 1438 هـ
أ / سمر السلمي

2. Outline for today Office Hours sixth homework due
Chapter Four :Differential Equations of The Special Functions
Legendre's Equation
Legendre Polynomials
Leibniz' Rule For Differentiating Products
Rodrigues' Formula
Generating Function For 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 sixth Homework
I put the sixth homework in my website in the university at Friday
homework Due Wednesday 22 / 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 Three: Ch 12, pg. 483
Legendre Equation & Polynomials, and Rodrigues' Formula
Section 2, pg pg 488
Section 4, pg pg 490
Leibniz' Rule For Differentiating Products
Section 3, pg pg 489
Generating Function For Legendre Polynomials
Section 5, pg pg 491

6. the Legender Functions
… (1)
….(5)
l constant
The general solution of the Legendre's differential equation ?

7. the Legender polynomials
(5)

8. the Legender polynomials
… (6)
the Rodrigues’ Formula ……(7)
We can find legender polynomial of l by repayment it in eq 5 , 6 or 7
And so ………
Find p0 (x) and p1 (x) from the Rodrigues’ Formula eq 7 ?

9. the Legender polynomials
Find p4 (x) ?
Find p2 (x)? Worksheet
Leibniz' Rule For Differentiating Products
Find
As we using binomial expansion
Writing the formula

10. Generating Function For Legendre Polynomials
(8)
(9)
Find p2 (x) from Generating Function ?
Prove eq 9 from eq 8
prove pl (1) = 1 from eq8
Prove from eq 9

11. Generating Function For Legendre Polynomials
Recursion Relations
………… (10)
Find p2 (x) from recursion relation (10.a)

12. Next class review
Legender Functions