You deserve an honorary doctorate, you have done more good than a lot of people who have received the honor in the past.

you are a big part of the reason why I passed calc1, calc2, calc3, and differential equations. thanks man.

Learned this 20 minutes before a test and aced this because of you. You’re the best.

PatrickJMT, I love you

You deserve multiple awards Patrick. Thanks a bunch.

I missed 2/3 of my lecture this morning. Thank God this video is here!

Patrick, because of you I made an A on my first DE test! I can't thank you enough

Thanks again so much! It's been over a year since I had series and sequences and didn't really have time to re-learn and go over series and I needed to learn how to do this quick. After trying some harder examples this made things click so thanks!

hopefully you also envy the huge amount of time i spent studying :) way way more than a typical college student i am sure.

@notstemmajor357

6 жыл бұрын

How much time did you spend?

you are killing it my brother. thanks a lot.

about what? what kept me motivated was an interest in math. i wanted to learn more cause i think it is a beautiful subject

as a math major...I envy your understanding of mathematics.

Another very helpful video. We just did this in my diff. eq. class today. Thank you for making it easier to understand.

Wow, that was actually a lot easier than I thought. Despite never having worked with power series before, I could follow your reasoning all the way (until the trigonometric functions was expressed using power series). Great video!

This a detailed intro to power series for LDE! Thank you!

Patrick! This is really helpful!! Thank you so much :)

You are really good at what you are doing.Thanks a lot

You're the reason I pass second year calc

Hey Patrick, I cant believe finally i have got to learn how to start summing from zero, that is what had totally made me lost.. u got a new subscriber lol...... thanks alot

Your videos always coincide with my curriculum :D

Nice job dude! That helps me a lot

Thank you so much for your help!

Thank you, Patrick

Legend! I had no clue on how to do these questions before....

Very well explanation... Thanks bro

congrats!!

You are still helping people to this day. My final is tomorrow.

Thank you patrickJMT

that was very helpful, thanks a lot.

It helped , thanku so much 👍

Easiest way thank you for this.

in our time, we learnt about Albert Einstein, Euclid, Galileo Galilei and Isaac Newton, fifity years from now-the next generation will be learning about Patrick! =)

Thank you so much!!!!! ❤️❤️❤️

Thanks a lot for the fantastic explanation. It saved my life in the final DE exam today. We should fire all the useless teachers and be taught by people like you. Thanks again.

This guy is a legend!💪💪

thank u so much! this sure helps a lot esp to those students who are self studying like me. C:

u saved my exam. thanks alot 😊😊

Thanks for saving me!

Patrick you are a math god, i worship you!

THe way you say the letter S is bothering me. But youre awesome!!!! I love you!

Patrick, can you explain how to do a power series with variables in it? i'm having a hard time getting the series to start at the same place when i input a variable and i just get confused. thanks! your videos are the best!

Thank you.

you are a god. Cant thank you enough.

Patrick do you have a video related with the singular points, ordinary points and radii of convergence?

Txs alot

love u patrick

Thank youGood explanation, I would like to learn the case for 2. order d.e however, we get only one linearly independent set of solution from power series solution i.e y''+y'=0 this is second order d.e there should be 2 set of eq. as well however from indicial eq. we get Cn and Cn+1 recursive and we can write the solution only with one set, so my question is that how can we generate second set of solution ?

For a question like this on a test, it would be much faster to jump straight to r^2+1=0, solve for r, and write the general solution in terms of sin and cos instead of using series.

@bizzless2308

9 жыл бұрын

Yes, the only reason you would solve it using this method is if it were specifically asked on the test. Otherwise using the general equation r^2+1=0 and solving for the complex roots would be much faster.

@rmiller415

8 жыл бұрын

I'm pretty sure this is seperable as well.

I'm trying to solve y"+9y=0 using power series. I get hung up with my odd terms. I can get it really close to sin(3x) but my coefficent causes a hang up. I can only get to this: C1(-1)^m(3)^(2m)(x)^(2m+1)/(2m+1)! How do I get my extra 3? to combine (3)^(2m) with (x)^(2m+1)

thank you

no problem!

Patrick , can u solve this ? power series involving diff equation y" - xy' + 2y = e^-x

thank you 😍

what would you do when there's a function of x infront of the y'' and y'? like ( y''-2xy'-y=0)?

THANKS !

This helped me a lot (even though it could go a bit quicker.xD). Thanks.:D

we are indebted to you

Thank u saved me

THANKS BRO

Patrick do you have a video related with the ordinary point, radii of convergences and singular points ? thanx

thankx a lot

THANKYOU VERY MUCH CAPT!! :') I got a good score becoz of u bruh

When we reach the part where we are extracting the middle part of the sum and finding values it could have to give zero, why are we isolating C_(n-2)? In all of the solutions I see to these sort of problems we solve to that, even when there are other C_n terms.

Hey Patrick, this example was great ! But I am stuck with a problem, Airy's equation, y'' - xy = 0. I am having trouble equating n = 0 to the summation limit of the two terms and at the same time getting X^n in each of them. Can you please please make a video on Airy's equation. I would really appreciate it.Thanks.

do you have a video on the power series of cosx, sinx, and e^x? thanks

Right on!

Thanks

What a pretty answer

I felt such a weird joy and satisfaction in the last 30 seconds.. I smiled all along. Must be the way religious folks feel when they pray to their deity. Anyway, I wanted to ask you something since you are probably the most fitting person I know for this. What are the best textbooks in these topics? (Multivariable Calculus, Complex Analysis, Linear Algebra, Number Theory and Theoretical Probabilities.) Thanks whether you answer this or not because your videos are great and always make me happy.

Patrick, thxn you so much. I was stuck with one problem that deals with summation n=1 to infinity switch to summation n=0 to infinity. You make it so simple to understand. The textbook didn't bother to explain x.X You should publish math textbook, must easier to understand d:D

I had this strange rendevous moment when seeing the cos and sin being those expressions

How do you solve about an ordinary point?

Why do you have to do evens and odds separately?

Oh I see, thank you!

at 7:58 can you ever start with n=a negative number, say you want to find Co?

whenever you see that and theres no initial condition it means the second derivative equals the negative of the fuction meaning it must be -sin x, -cos x, sin x, or cos x, because those functions second derivatives are the nrgstives of themselves. it could also be something else im not aware of i suppose

Hey man please can make an example of solving this type of equations :S y"+f(x)y'+g(x)y=r(x) Thanks man

any examples with the y", y' & y altogether?

yes! it normally does not work that way :)

thanks :D

n is a constant, x is the variable.

is that a singular point or ordinary point?

what if the powers of the x are not the same, and are a bit more complex than this, can we still use this method? am finding it a bit tricky..

What if you're given an initial value for a? (or in your case, c, such as c=0) edit: given a solution centered at a=0

at 2:18 does anybody know why when he took the derivative of y' = Cn*n*x^(n-1) he only has the derivative of x^(n-1) in y''? There's also another n there in y' so why isn't he taking the product rule of it in y''?

This really helped me out, but dear lord I hope you have a better microphone now.

@patrickjmt

7 жыл бұрын

i dont

@decodeddiesel

7 жыл бұрын

patrickJMT Maybe it was because I was listening with headphones, but it was hard to watch due to the lip-smacking and popping. Still though, very helpful. Thanks.

@thor-sonofodin6177

7 жыл бұрын

lol

Could you possible solve this one: Find the first 5 nonzero terms of the solution given the IVP, y''-xy'-y=0, y(0)=2, y'(0)=1

Very easy need hard questions

dat mic breathing tho

@ahmedislam3007

9 жыл бұрын

Alex Coulthard he's awesome at maths though, he's the Darth Vader of math man lol

@joeyGalileoHotto

4 жыл бұрын

Final Exams in a Nutshell LOL

my original eq is Y'' -(1+x^2)y =0 in the end i still have an x^2 that i cant put values in like you do with n, what should i do in this case?

@GabrielSanchez-yw7hr

10 жыл бұрын

all you have to do is for the -(1+x^2)y is factor the negative so (-1-x^2)y and then you’d have -1*summation c_n*x^n) and - summation c_n*x^(n+2) in order to get an x^2 term when n=0

May god bless you

Aren't you gonna define what c0 and c1 in your answer? Also, do you have an example of a differential equation involving y^2? I've seen answers to this kind of problem and they are not stated as compact formulas.

nice

good

For the x that you factor out of the series, does it always have to be x? Can the x you factor out be x^(n+1) ?

@Avo4

8 жыл бұрын

+Brandon Rodriguez Thats where the idea of changing the indexes of the series so that all x^(something) can be factored out as the same x^(something)

@rmiller415

8 жыл бұрын

You can only factor an X because there is no n associated with x^1, the x^n term has to stay inside of the summand.

Frobenius's Method soon?

13:47 When you were breaking the equation into its odd and even components, weren't those the components of y"+y?

@Plagueborne

4 жыл бұрын

The solution is a solution of y, just like most other linear first/second-order ODE's we study.

Thank you so fucking much man

king

Why do you start using m half way through? Just keep using n...