Mathematics 2 The thirteenth and fourteenth Lectures The tenth week 12 - 16/ 7/ 1438 هـ أ / سمر السلمي

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

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 (https://uqu.edu.sa/smsolamy) , so please check it my email is smsolamy@uqu.edu.sa for any question. every Wednesday a homework will be submit at my mailbox (or email 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 11-12-13 / 8 / 1438 h every in her group

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 email in the same day than put the paper next day in my mailbox

Chapter Three: Ch 12, pg. 483 Legendre Equation & Polynomials, and Rodrigues' Formula Section 2, pg 485 - pg 488 Section 4, pg 489 - pg 490 Leibniz' Rule For Differentiating Products Section 3, pg 488 - pg 489 Generating Function For Legendre Polynomials Section 5, pg 490 - pg 491

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

the Legender polynomials (5)

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 ?

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

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

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

Next class review Legender Functions