Using the convolution theorem to solve an initial value prob | Laplace transform | Khan Academy

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Using the Convolution Theorem to solve an initial value problem
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@estebanlopez1701]

I love Sal. One of funniest things about him is that he is an MIT graduate who admits getting confused while teaching, I think that makes learning from him so pleasant because you do not feel that stupid when you don't get things right away

[@bbcbigblackuknowifuknow1148]

💯🤭❤️

[@gh.adithya]

I struggled with physics over the past year in college, mostly due to my math being weak and not being taught well enough at my uni. This playlist helped me so much, watched all 45 videos over the past few days. Thanks a lot Sal, very grateful for your effort and dedication.

[@GamjaField]

Can you do the video about Fourier series someday?

[@williammelendez-suchi5546]

thanks to your amazing video series, i was able to understand the fundamentals of Diffetential Equations before taking the actual course. I ended with an A in the class, and recommend to all my friends these videos. thank you for everything!!!

[@MrDevin666]

Omg i'm not at this level in calculus, but i still enjoy watching videos of stuff that's complete 'Huh?" for me, lol you're awesome and ingenious in so many ways that cannot be expressed in words, only gods can comprehend the intellectual power of this man's knowledge.

[@fawzyhegab]

I have finished this list now . I hope you add more videos on Differential equations , this would be great :) you can explain approximations methods for solving DF . thank you very much for those great Vids :) Greetings from Egypt!

[@EvanBouchard]

After over one full decade, I have finally found the most useful thing on the internet. One hundred cocktails to you, sir. Thankyouthankyouthankyou.

[@MrPFrizzy]

Thanks Sal. Great explanation on all 45 videos! RESPECT!

[@xadrez1348]

45?? i found just 20

[@huizeguo6294]

i wish someday i can a be a teacher like you, explain complex stuff in an easy way

[@sisip123]

awesome! i'm cramming for a differential equations test tomorrow. that was really helpful! thank you.

[@mooeoo]

Finished all this 45 videos in 4 days. It was very clear. Thank you so much Sal. I would appreciate if you give us some examples with real life application.Such as that Spring which is mentioned in this videos. Thanks again.

[@shahrukhtramboo6781]

Thank you sir for the lessons. you made my day.

[@MartinVincentBloedorn]

Excellent explanations. Keep up the amazing work. You're saving my life as a calculus student, and that's for sure ;D

[@SuperSpawn1995]

so long and thanks for all the fish

[@rafafdz]

Sooo its 4 am and my exam is at 8:30 am... I started watching this series like 2 hours ago. Wish me luck

[@anilturan4170]

so what happened dude :)

[@Cashman9111]

he died I guess

[@cansabanci]

@@Cashman9111 nobody comes back here after exams finish...

[@8kubera]

he must be celebrating still...forgot to come back and say thanks

[@Flopsaurus]

Thanks for everything Sal!

[@hddevani]

Hey will you please make videos on partial differential equations ( wave , heat , --laplas , diffusion ) ..and solutions for it...

[@mikebaee7731]

Thanks, this is exactly what I was looking for...

[@xadrez1348]

thanx u did great help

[@Tessastiel]

Very useful, thanks

[@landofbooks4426]

WOW. There are a lot who watch your videos to understand calculus. I watch your videos to become like you !

[@SandeepSingh-qr3dk]

thank you sal. just watched your last video on lapalce transform.

[@joshmeiyb]

Thank you Sal,I've watched the whole 45 videos, it really helps a lot!

[@stephaniesingh14]

I'm only seeing 20. pls help

[@12804olivier]

thank you sal

[@Kosekans]

After now having watched these 45 videos, i'm seriously a bit sad, that this was the last one for now. But let me say, if you decide one day to continue this videos about differential equations or other higher mathmatics stuff, no matter if tomorrow, in one year or in five years ... i'll be sitting here waiting ;-) Thanks a lot for the excellent explanations.

[@uzumo4870]

what about 11 years dude

[@arimakousie5612]

Thank you very much , indeed it means a lot , and helped a lot, greetings from japan

[@sassanmokhtar4481]

Thank you Sal.

[@annadourneva8348]

Thank you!

[@PMTcommenter]

You're AMAZING!!!!!! Thank you so much!

[@samehum]

Hi Sal, Can you please do APPLIED MATHEMATICS videos

[@elenizotos3359]

Thank you!!!

[@mrKreuzfeld]

you would not mind making a lecture series, on soblev spaces? :P I like your vids, keep up the good work (btw that was a joke about asking you to make lecures on soblev spaces, it would probably be only me that would use it)

[@sstl517]

You could have used a table of Laplace transforms and looked up the inverse Laplace of 2s/(s^2+1^2)^2 ==> 2(t(sint)/2) = t(sint) so y(t) = t(sint) when y(0) = 0 and y'(0) = 0 and find constants C1 and C2 The point of using Laplace transforms is to avoid convolution in the time domain.

[@happyhedgehog6450]

Awesome videos here. Thanks Sal.

[@phamhatrang8652]

Thank you so much

[@asif7240]

Thank you so much!!

[@haydenstephan1489]

Finished the playlist! I don't even need this, I just love learning math!

[@lukapopovic5802]

Hayden Stephan haha same

[@dienefordelta]

i have an exam in 20 mins. I've watched almost all of these and I honestly feel well prepared now. Thanks so much!!

[@aneeshprasobhan]

so what do you do now ?

[@VeXorian1337]

Hi, I'm still missing the point of convolution when solving differential equations. Ok, I got the idea that if you take the convolution of the original signal with the impulse response of a transfer function, you actually get the new processed signal. But how is that easier to actually solving the equation, when you can just do partial fractions and solve it even faster and easier? Still it was a nice series of lessons, that explained what convolution is, for which you have my thanks :)

[@emelefendi1]

i am so sorry to not being here before...you are a great teacher nice job really

[@phathumanugu3757]

Great, hoping 2 pass

[@jahanaraparveen9436]

can you do a video on series solution??I will grateful if you do so

[@jeannnliao9406]

thank you Sal!!!

[@kubilaybayindir8684]

Thank you for everyhing :)

[@fakhriadk]

I procrastinated and only gave myself 2 days to study this. I'm screwed 😩

[@mwm48]

...how come i can rarely get ANY of your videos to display more than blank screen, this seems to happen more often than not. does anyone have any info on how to resolve this problem? :( btw, the videos that decided to work were very informative, especially since my professor's English is kinda rough, thanks for the vids!

[@bonbonpony]

Can it be also used for solving differential equations with NON-constant coefficients?

[@geethsameer614]

I wanted to know about this, but I couldn't find much info anywhere

[@Kosekans]

Yes of course I am ... ;-)

[@juanvaldez4169]

I love you Sal !

[@PlanterSanSama]

Never have I understood a video while laughing at the word "thingy"

[@TheSa7777]

@Kosekans It's been 2 years. Are you still waiting?

[@J0EH3AD]

Thoug I love mathematics, I have no idea what these things mean.

[@DavidKlausa]

@mapleleaflover89 you're = you are

[@michaelempeigne3519]

you stated at 5:23 "that's this term right here" when in fact that it is complied of two terms.

[@skepticmoderate5790]

So what?

[@DeadbeatXT]

you're

[@paoboonjinnz]

sorry my professor wanted students to solve all the way down to the end.

[@alxjones]

You never mention that if you have a convolution f*g then you can equivalently use g*f. That would simplify this integral a bit, as it would be integral e^(T)sin(T)sin(a(t-T))dT. Not that it's solvable, it would just look a bit nicer. Sometimes it CAN be the difference between a solveable and unsolveable integral.

[@AzizSobirov]

Thx for your compliments but if my name is Aziz it doesn't mean I am Arab it like saying all muslims are arabs.

[@TasneemSTEM]

WE are all brothers

[@AzizSobirov]

Hey I am 17 and finish all the video in 2 days

[@DelphianSociety]

.Yes, it's a stupid name .

[@x4yuf4nx]

you are amazing. will you marry me?

[@hddevani]

Hey will you please make videos on partial differential equations ( wave , heat , --laplas , diffusion ) ..and solutions for it...