Solving ODEs by Series Solutions: Legendre's ODE

In this video, I solve the Legendre differential equation, using the regular series solution method.

Questions? Let me know in the comments!

Prerequisites: Series solutions intro video, Basic Calculus, Really basic ODEs (first order ODE stuff)

[ColinBundschu]

I'm a grad student in applied physics at Cornell, and these videos are the first time that someone has lectured math in a way that makes sense. This is life changing.

[HidrogenoyMau]

You're a godsend, you're literally the reason I'm passing Advanced Math for Physics this semester, thanks a lot!

[ksorv]

You rock man!
BTW speed is unnaturally fast which suits the mathematical things you say...
Keep on doing good work, I will get a good grade in maths

[KhushbooGupta-hmdg]

please please pleaseeee
make video on generating function for legendry equation,
hermite and its all equations..
humble request..please...
ur videos are really helping me for my exams...

[shmakn]

Found this 10 Hrs before the quiz. Thank You!

[huishansun]

thank you so much!! i am studying nuclear reactor analysis and this video saved my life.

[kostasfykouras]

hello! Great video as always. One question though. For k=1 the solution is in terms of odd coefficients and for k=2 in terms of even coefficients. So we say that the polynomial created by those even/odd coefficients is the solution. But, for k=1 we also have the even series that doesn't terminate. The even series for k=1 isn't an acceptable solution?
We just disregard it ? Thanks in advance!

[rahiabrar]

I'm an undergrad at a pretty reputed indian university but what wonders me is the fact that the faculty here despite pretty qualified and paid a handsome amount money don't possess even 0.0001% of teaching skills that you have. I literally skipped most of my math lectures because the professor's teaching style was such bogus that i lost interest in the subject. This video was a lifesaver for me.

[MF.G.D]

Shouldn't the index changes as you differentiate?

[daniellebest]

you are the person who will be responsible for me passing mm3

[anoopdahiya]

Can someone tell me which software he is using for writing purpose??

[alaaooo]

When you started to take the derivative of the power series at 1:49 you should start the summation from 1 for the first derivative and from 2 for the second one

[ArthurMorganFTW_RDR]

why are you not starting sums of y' from n=1 to infinity and y'' from n=2 to infinity because n is 0 at n=0 and (n-1)n is 0 when n=0, 1?

[dhatridongre]

I love the hint of comedy in your videos. Thank you for these videos. They are so clear and easy to understand

[tanishphopalkar]

Very nice playlist explained in a concise way! thanks alot

[overlordprincekhan]

A fast-paced video which perfectly explains the math? Damn man, this is some next-level stuff. Bro, keep up the good work. I wish you my heartiest wish for your development of this channel.

[maxmalakjan]

Ok can you help me out here? Why do we not consider the infinite series in the Legendre Polynomials? So e.g.: if k = 1, then why do we not consider the even series?

[debdarudasgupta]

for first and second derivative the starting value of n should change right ( 1 and 2) respectively, in order to make the function defined . But its not have been done, any specific reason ?

[kiddomonkou]

y' should be from n=1 to infinity and y'' from n=2 to infinity, right? Correct me on this if i'm wrong.

[adonisbibat]

hi @Faculty of Khan, please enlighten me. when you assign a value for a0 & a1, is there an exact step to do so? coz if i pick different values. it will end up different formula. are there any ways to determine the exact value of a0 = -1/2 ?