11.1: Orthogonal Functions

[@valor36az]

Many thanks for the comprehensiveness and clarity, this explains so much of the Fourier series

[@alidiwan1208]

Currently preparing for DiffEq2, and this is helping tremendously. Thanks a million!

[@putin_navsegda6487]

God bless you Madame ! Your videos are really good and helpful !

[@simgauvin20]

at 10:52 The result of the integral in front of the sin(nx) should be 1/n and not 1/pi right?

[@alexandraniedden5337]

Yes, you are correct. Good catch!

[@holyshit922]

I wrote program using Gnu MultiPrecision library
for generating orthogonal polynomials via Modified Gram-Schmidt and inner product
It seems that it requres O(n^4) floating-point operations and O(n^2) space
but recursion from ordinary differential equation requres O(n) floating-point operations and O(n) space
if we need only one polynomial and O(n^2) floating-point operations and O(n^2) space if we need all polynomials of degree up to n
10:56 Here should be 1/n instead of 1/pi
11:24 cos(mx)cos(nx) if we forget identitty for this product we can derive it using angle sum and angle difference formula
cos((m+n)x) = cos(mx)cos(nx) - sin(mx)sin(nx)
cos((m-n)x) = cos(mx)cos(nx) + sin(mx)sin(nx)
and we can add them up
but if we forget these formulas we can still integrate by parts

[@rayaden_17]

great video helped a lot!

[@EamonnO]

Brilliant simple answer to what I was working on and there is an error in the text book. Thankfully I suspected that..hopefully some new students are not going around in circles.

[@xturkishsa8092]

am glad I found ur channel.

[@mianworks]

The lecture is life saving!!!

[@theundergraduatekemist4077]

You are a life saver

[@TheAttic22]

Very helpful indeed. Thanks a lot!

[@al-barakah]

Thanks for the effort ❤

[@jc3361]

thn you so much for this amazing explanation! and i confuse that... i understand norm of 1 and cos(nx) is sqrt(2pi) so divided by sqrt(2pi), but why it can be 1 for it now multiplied by cos(nx)/sqrt(pi)?

[@muwongeevanspaul9166]

Madam Alexandra...thanks for your effort but am wandering how u come up with a zero without considering the fact that sine of a negative angle is negative sine of that angle. High light me please in your ex 2. Also in example 1, how did u come up with 1/pi????

[@nabilahhannani4899]

thanks a lot for the video, may I know why cos mx . cos nx dx = [cos (m+n)x + cos (m-n)x] dx ?

[@preethikumaris8079]

Thank you very much mam. Gave Amazing understanding of the subject.

[@deanekennah]

Thanks a lot, nailed it, but please why is the integral of x^5 from -1 to 1: 1/u (x^6)

[@alexandraniedden5337]

If you take the derivative of (1/6)x^6, you will get x^5. You are "undoing" the power rule.

[@deanekennah]

hmmm, yeah thanks a lot Miss/Mrs Niedden

[@ieimagine]

Thanks!

[@mohammedalshannag6098]

amazing

[@mnooolalharbi2954]

Which book is this from? Please

[@alexandraniedden5337]

Zill's 9th edition Differential Equations & Boundary Value Problems.

[@mathmath3021]

if u hv a book send it to me plz

[@danceproduction170]

is its solved exercise available there I mean solution of 11.1

[@danceproduction170]

thanks dear but these are solved examples and I want solved exercise of these examples from th book differential equations with the boundary values problems by zill

[@danceproduction170]

exercise is 11.1

[@abdullahtauqeer5405]

Thank u

[@muwongeevanspaul9166]

Sin(-x) equals to the -sinx.... Madam high me on y u don't apply that principle and u just fall on a ZERO

[@kylevebar3909]

Fml

[@Shubham-jy8ki]

Hiii

[@johncrosschukwujekwu1600]

You're skipping some steps🤦🏾‍♂️

[@areeburrehmankhan1166]

Like? I would love to know so I don't make any mistakes while I am learning.