Started the video, paused, went to my marker board and solved it! Then skipped to the end and I saw that I got it right. First time I have solved one of these on my own. Your help has been HUGE! Thank you!

@blackpenredpen

6 жыл бұрын

I am very glad to hear this!!!!

Spent the last week panicking about Laplace transforms - all of that anxiety vanished after watching this video! Thank you

@blackpenredpen

4 жыл бұрын

Glad to hear!!

You just taught me more than my professor taught me in a whole semester❤

学到了啊 待定系数还能这么拆 很棒的细节讲解

Seriously one of the best teachers I've ever encountered both on youtube and real life. I salute you! Thank you for explaining every detail of your solving and making sure we understand every step you take

thank you so much for explaining where the partial fraction decomposition comes from!

Your tutorials are the best just that I'd like to comment on this and a previous video about this same IVP that you should note the way you write your (Y and y). It conflicts as to know which is the laplace and the inverse laplace, Just to help amateur like me. Thank you for your best explanation.

your video makes concept crystal clear

i am a student on uni. at south korea. thx your class. it a big help for me.

I dont really know why professors in my uni just does not go into this much depth into explaining a single example. The way he teaches me reminds me of my high school teacher who used to make complex problems easily digestible.

Just for the sake of trying the convolution formula i solved the partial fractions s/(4+s^2) + 2/(4+s^2) + 1/[s^2(4+s^4)]. Nice!

Watching this during my Calc 4 exam, thank you very much my dude

Lots of love for you sir.. 😍😍😍 From Bangladesh.. Your method was super easy to get the problem..

woaahh i never knew laplace is this easy..thank you sir, tutorial appreciated!

I want to comment that you can use residue method to get A/s. To do so, we will consider P(s) = (s^3 + 2s^2 + 1)/(s^2 + 4). Then, we can differentiate P(s) but we have to divide it by n! where n is the number of times differentiation can occur. (In this case, n= 1) because s is only repeated once. P'(s) = [(3s^2 + 2s)(s^2 + 4) - 2s(s^3 + 2s^2 + 1)]/(s^2 + 4)^2 From the previous cover-up: s = 0 so we have P'(0). Then, you can plug 0 into your function. After applying differentiation. You'll be surprised you'll get the same answer for A.

I don't sub often, I am about to graduate this year and you earned it!

Absolutely perfect job. Thanks!

Bro thanks so much for all youve taught me, in this case wouldn't it have been easier to solve using method of unconfirmed...

You're a good tutor! Im about to comment because i got confused in the A/s +B/s2 ... but you discussed it well ahhaha slow clap*

Great work! Technically shouldn’t all of this be multiplied times the unit step function, which would be the same as saying “for t >= 0?”

Dude You are the best !!!!!! I owe You 20 Marks!!!

@blackpenredpen

6 жыл бұрын

Thank you!!!!!!!

You've helped me a lot thanks

Me gustaría entenderte en el idioma pero observando tu procedimiento me a ayudado, gracias

Thanks a ton, now I feel very motivated

You can use cover-up to solve for C and D. Just make s=2i and substitute in. You get 2i+(-7)/(-4)=2i*C + D, therefore D = 7/4 and 2i=2i*C, thus C = 1. BAM!

Thank you so much dear Teacher 💖

Great job man, really good explanation. I think whats so hard to understand is how the denominator is split up into A, B etc. I've taken earlier courses that covered it, but not in the same extend that these exercises need.

@harleyspeedthrust4013

3 жыл бұрын

look up "partial fraction decomposition"

this guy saved my life

This vid helped me more then books

is there a playlist for this kind of problem's?

Sorry man but I had to.... Pause the video to comment and give you a thumbs up! So glad I subscribed, great work!! Thank you!!

Thank you so much!😭😭💕💕

Yes, I just said "isn't it?" just like Y O U ! ! !

@blackpenredpen

6 жыл бұрын

Yay!!!!!!!

Thank you

Love this!

this deserves more likes than those useless travel vlogs

I can't find your Laplace playlist.

Bedankt maat!

wow. thank you

thank you

If that s³+2s²+1 was s³+2s²+s, you would do: s³+2s²+s=s(s²+2s+1)=s(s+1)²

The best

your voice is asmr to my ears

very kind smile

Is that a microphone

Aha! You want to look the 4 as 2², isn't it?

Math is beautiful

Weird thing. My teacher use this equation in our assignment

@xxslysinxx

6 жыл бұрын

Did you write your answer in black pen and red pen?

Best way to solve DE is with Laplace Tf

@harleyspeedthrust4013

3 жыл бұрын

agreed, unless u dont have initial conditions then my favorite way is variation of parameters

Very good

@manyielkoth2221

4 жыл бұрын

As long as you are getting him

I distinguish my s and my 5 using cursive handwriting

may i know why so i have to add CS + D and your peevious dont need?

@carultch

7 ай бұрын

For linear terms, you only need a constant for the numerator. For irreducible quadratic terms, you need to set up a linear term for the numerator. If you had an irreducible cubic, you'd use a quadratic term for its numerator. It wouldn't help you very much for either integration or Laplace transforms, but that's what you'd do in concept. In general, the polynomial on the top, is one degree less than the polynomial on the bottom. Sometimes, the linear factor turns out to just be a constant, other times, the linear factor turns out to only be the term with the variable

that pen swish doh 15:10. Swag

5:00 20 seconds does not equal 50 seconds unless we are moving fast away from each other and relativistic effects take over.

What is the laplace of sint

@carultch

8 ай бұрын

1/(s^2 + 1) Cosine has the s up top, sine has the constant.

I found "A" to be 1/2 no zero

I love youuuuu

ليه حطيت T=1/s^2 ???

@tarekkhalifa8634

3 жыл бұрын

why ?

Pointing out the seemingly obvious, but you forgot to multiply by 2 inside the cosine inverse LaPlace and the 1/2 outside, so it should be 1/2* cos(2t)

@blackpenredpen

7 жыл бұрын

Steven Tucker u only have to do that for sine. Cos is ok

how we can get D=7/4 like how 2 become 8/4 - 1/4 = 7/4 just how that 2 become 8/4 sorry if my question is so complicated .

@carultch

7 ай бұрын

Given: (s^3 + 2*s^2 + 1)/(s^2*(s^2 + 4)) I like to set up the terms for Heaviside coverup first, which in this case is A: A/s^2 + B/s + (C*s + D)/(s^2 + 4) At s=0, cover up s^2, and find A: A = (0+0+1)/(0^2 + 4) = 1/4 Reconstruct: (s^3 + 2*s^2 + 1)/(s^2*(s^2 + 4)) = 1/4/s^2 + B/s + (C*s + D)/(s^2 + 4) Multiply by s, to partially clear the fraction: (s^3 + 2*s^2 + 1)/(s*(s^2 + 4)) = 1/4/s + B + (C*s^2 + D*s)/(s^2 + 4) Take the limit as s goes to infinity, to set up our first equation: 1 = 0 + B + C B = 1 - C Pick two values of s we haven't used yet, to create two more equations. I'll choose s=1 & s = -1 s=1: (1^3 + 2*1^2 + 1)/(1^2*(1^2 + 4)) = 1/4 + B + (C + D)/(1 + 4) 4/5 = 1/4 + B + (C + D)/5 20*B + 4*C + 4*D = 11 s = -1: ((-1)^3 + 2*(-1)^2 + 1)/((-1)^2*((-1)^2 + 4)) = 1/4/(-1)^2 + B/(-1) + (C*(-1) + D)/((-1)^2 + 4) 2/5 = 1/4 + -B + (-C + D)/5 8 = 5 + -20*B + 4*(-C + D) -20*B - 4*C + 4*D = 3 Add equations to cancel B & C terms and solve for D: 8*D = 14 D = 7/4 Use original equations to solve for B&C: 20*B + 4*C + 4*7/4 = 11 5*(1 - C) + C = 1 -4*C + 5 = 1 C = 1 B = 1-1 = 0 Result: 1/4/s^2 + (s + 7/4)/(s^2 + 4)

His using 2 markers one hand

This is so tough

not difficult, but very easy to make a mistake

I don't understand at 6:45

@hanaa.r_

7 ай бұрын

How when 1/4 we put in A

hm, so you don`t use the +1...

@5stepshred300

6 жыл бұрын

Good observation, did you forget to use the +1?

@blackwatch7572

4 жыл бұрын

hahahahaha temos um ancap por aqui.

Worst way to solve a linear ODE. How about a non-linear ODE example?

@blackpenredpen

5 жыл бұрын

Hi Rob!

@jammcrusader1981

4 жыл бұрын

lol dude - its about learning the method

@harleyspeedthrust4013

3 жыл бұрын

dude its just an example to get the hang of laplace transforms chill out dickwad

The way you do partial fractions doesn't make a bit of sense...

@blackpenredpen

5 жыл бұрын

Which part confused you?

@joshuamitchell359

5 жыл бұрын

@@blackpenredpen Actually, I totally confused myself while I was doing the problem along with you. I missed an "s." It made perfect sense! Sorry about the inconvenience!

@blackpenredpen

5 жыл бұрын

Joshua Mitchell I see. 😎

Literally the partial fractions is so unnecessary and it takes up over half the video, without taking the common denominator and keeping it as three seprate fractions we coud have taken the inverse laplace much easier with a VERY easy convolution to solve at the end

@harleyspeedthrust4013

3 жыл бұрын

yes but in general you want to avoid convolutions. the point of the laplace transform is to solve the problem without actually doing calculus, so if you can find partial fractions then you should do that instead

But… no.

His English is so bad

@harleyspeedthrust4013

3 жыл бұрын

better than yours

Thank you