👍🏾 Great explanation

Nice work Dr🎉

amazing

very helpful

yeah amazing work, precise and clear, I love it

This is interesting and informative.

Great explanation

Hi! Can i ask what pdf document you are using? What book is it from? Would you be able to share it?

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Great explanation, thank you so much sir

I derved fomula in two ways both universal for orthogonal polynomials 1) from recurrence relarion 2) from ordinary differential equation Way presented on this video is maybe shorter but possible for Chebyshov polynomials only Ad 1) I derived recurrence relation the same way as presented on this video but i solved it in following way * I defined exponential generating function (ordinary generating function gives me trigonometric solution from which i started) * I solved ordinary differential equation with initial conditions via Laplace transform * I got exponential generating function E(x,t) = exp(xt)cos(sqrt(1-x^2)t) (Here wikipedia claims that this is hyperbolic cosine but x is in [-1;1] so trigonometric cosine is better because avoid imaginary argument) * I calculated nth derivative of exponential generating function via Leibniz product rule and evaluated it at t = 0 Here I went further and used binomial expansion and got double sum * In this double sum I reindex inner sum and then changed order of summation Ad 2) I started from T_{n}(x)=cos(narccos(x)) Let t = arccos(x) y(t) = cos(nt) y'(t) = -nsin(nt) y''(t) = -n^2cos(nt) y''(t) = -n^2y(t) y''(t)+n^2y(t)=0 Here I used change of independent variable t = arccos(x) and i got (1-x^2)y''(x) - xy'(x) + n^2y(x) = 0 Now i used power series solution to sove this equation I got recurrenece relation for sequence of coefficients I splitted this sequence into two subsequences (for even and odd terms) I expressed values of these subsequences in terms of product and then i combined them into one sequence If we have two sequences a_{m} and b_{m} and we want to merge them into one sequence c_{m} such that a_{m} are even terms of sequence c_{m} and b_{m} are odd term of c_{m} then sequence c_{m} can be expressed as c_{m}=(1+(-1)^m)/2*a_{m}+(1-(-1)^m)/2*b_{m} There are Chebyshov polynomials of the second kind but they can be expessed with first derivative of Chebyshov polynomials of the first kind Itcan be observed that leading coefficients of T_{n}(x) = 2^{n-1} it is actually not true for n=0

very informative session

Interesting

I index the coefficients of numerators so i have not problems with lack of the letters in alphabet

Done! Thanks for Clear & precise explanation Mw.

I have 15 years temperature data. How can I determine the trend by using these temperature data?

Good explanation sir, in third example while find y you take +ve sign in place of -ve sign

One of the best lecturers in existence.... best explained

Good explanation.. thanks

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very educative.

Informative 👍

Great work sir. I just love how elaborate you are.

Get the Video transcripts here: drive.google.com/file/d/1TdzBpYO3E0WhxXsk9s09ZGMsr5mHDX01/view?usp=sharing

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Good content.🙂

The content is clear and informative.

I really learnt a lot. Thank you Dr. Mutuguta

This is great sir... thanks alot

I remember this method

plus and minus symbol in matlab???

Professor 💪💪

Proud to be in your class back in the days, God's speed

keep winning

Good content Dr. , I enjoyed your teaching methods.

symbolic maths 👍

I would love to learn this too. Thumbs up to my COD

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It's phenomenal for you to impart me with a lot of knowledge , sir . Receive deluge of blessings from God.

This is interesting. Simple and easily understood. nice work

nice work Dr.

Reading my notes while listenig to you. This is an amazing explanation sir. God bless you

Nice one daktari