Laplace Transform of a Piecewise Function (Unit Step Function)

In this video we will take the Laplace Transform of a Piecewise Function - and we will use unit step functions!
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/ @brithemathguy
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#laplacetransform #brithemathguy #math

[@BriTheMathGuy]

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[@LcWorlx]

Hi, in 4:37, why did it became {t+1} ? Is it because there is a (t-1)? So we should just write the opposite of its sign? If it is (t-2), does it become {t+2}? What would happen if it is (t^2)?

[@jamesvarner7816]

Not only does he explain step functions in a way anyone can understand, he write it all backwards. This man is not human ...

[@amangoheer8824]

He's obviously writing normally and then inverts the video. Use some common sense

[@jamesvarner7816]

@@amangoheer8824 A non a-hole would have just described how that is done instead of just being an a-hole, but as you are clearly an a-hole, I guess you were incapable of that. Meanwhile what you said didn't make sense. His back is to a white background while writing on a window, with the camera on the other side of the window facing him. You can clearly see what he is writing in front of his hand, not hidden behind it. Unless you are talking about meshing video layers in post-production (which is also a nice trick), what you described would still come out backwards.

[@viviankamanga1650]

I low-key love him

[@aimeeh2079]

@@amangoheer8824 Fun fact actually, due to the wall being transparent it is actually always going to look the right way compared to something opaque. You can see as such when you write on plastic in front of a mirror, you can read it both in the mirror and from your original position. It's real interesting I think Vsauce did a vid on it once

[@MotoREEngr]

Others: Writing infront of the board Him:writing behind the board.. Great explanation tho

[@BriTheMathGuy]

Thanks very much!

[@mohit9028]

@@BriTheMathGuy hey ! you are actually writing mirror image or election form haiii !!

[@mohit9028]

reflection*

[@BriTheMathGuy]

@@mohit9028 I'm writing normally, it's video editing :)

[@thisguyispeculiar]

Super helpful video. I was having a tough time wrapping my head around how to convert piecewise to unit-step and then write its laplace. You made both steps easy and approachable. I am going to use the light switch analogy every-time I get confused, lol.

[@brianhoran9868]

This makes everything about the Heaviside function seem so simple...Thanks my guy! I really appreciate it!

[@seasnek7024]

Learnt more in 6min than I did for over an hour with a similar tutorial Your version of solving it is so much better and coherent. Subscribed

[@dannybrowning501]

Excellent video! You really helped me out in my advanced engineering math class; my professor has an "interesting" teaching style.

[@BriTheMathGuy]

Glad I could help!

[@monoki8708]

SAME

[@Cartoon_Physics]

You guys weren't at U of I, were you?

[@aez504]

No

[@reeseromero5688]

What a freakin stud; made this idea so easy to wrap my head around. Thanks man!

[@BriTheMathGuy]

Glad to help ya out!

[@sheriffalidu5182]

No confusing sketches. Just straight to the point thank you

[@dylansinclair7751]

This guy has just taught me how to do a problem in 6min that my math lecturer couldn’t teach me in a month

[@JOAE23]

After searching for every video for unit step function and not understanding a single thing, you made it so much easy to understand( the switch on or off idea make it so easy to grasp😂

[@abbylong8172]

Thanks so much!!!! I took DE a year ago and now I'm doing Laplace Transforms in mechanical design!!!!!!!!!!!!!!!!!!!!!!!

[@mohammedmuneeb6888]

Taking differential equations in Summer and my professor (while really good in his work) is rushing pretty fast through the content. Thank You for the video, solved my doubts.

[@IceInsightss]

I spent 2 days figuring this out and I finally got it 1hr before my exam starts. Now I’m gonna make sure I don’t forget! Thanks so much for the help

[@konstantinshterev2860]

i hope u failed ur exam

[@amazingweatherupdates9082]

Thanks for the help! You really explained the Laplace transform well. I like the "light switch" analogy for the piecewise functions

[@BriTheMathGuy]

Glad it was helpful!

[@I0MSammy]

Legend. Watched 4 other videos explaining this subject but nobody else explained how to do it with a function multiplied by two step functions!

[@ztwill17]

I'm late to the party, but this was great. Exactly what I needed as a supplement in a 6-week 4 credit summer class!

[@ElijahAndrade01]

This was a lot of help. Its amazing how having something properly explained makes math easier, unlike the magic my "professor" was doing. Thank you so much for clarifying

[@kedarparab8001]

You are the only guy who explained how to any function to unit step function. Thanks

[@BriTheMathGuy]

Glad to help!

[@timothysands5537]

I was so focused on how he setup the camera so that he could write and the letters don't come up backwards, that I had to re-watch the video lol. Good explanation on the building of unit step functions using piece-wise functions, thank you!

[@wamid455]

GOAT. Better than Dr. Bazett, since instead of giving impossible terms to understand, you have explained it with simple words

[@JosueBenitez-eg4cz]

thank you so much, I was banging my head against the table trying to figure out how to set it up.🙏

[@walterbirdwell3675]

thank you so much for your videos. Examples are how I understand the content best, and you explain this in a much more clear and concise way than my professor.

[@BriTheMathGuy]

You're very welcome!

[@anjana_nath9081]

Thank you so much for putting out the fire in my head. Super explanation. Thank you sir.

[@stoup8778]

This was the only explanation that I could make sense of... thank u very much bro

[@jaikowalik966]

Keep up the great work BriTheMathGuy, you saved me on my assignment! Very understandable and succinct explanation.

[@BriTheMathGuy]

Glad I could help!

[@patpat1982]

Out of all the videos I watched, this one got the best content.

[@azyle2104]

You're very articulate , could listen to you all day

[@milesseminario5933]

I had to miss the class where we went over piecewise functions, this is amazing

[@nped5054]

This is a great video, but when I'm using your method with an example I'm working with, it doesn't really make sense for me. How would you solve the unit step function of f(t)=sin(3t), 0 < t < pi?

[@christopherpayne7650]

sin(3t)*(u(t-0)-u(t-pi)) --breaking it down to the step function = e^-0*s * L{sin(3+t)} --anything raised to the zero is 1 so you just solve the Laplace of sin (3+t) using a trig identity, L{sin (3+t)} turns into L{sin(3)*cos(t)+cos(3)*sin(t)} sin (3) and cos(3) are constants so they can be pulled out you're left with : sin(3)L{cos(t)} + cos(3)L{sin(t)} and the Laplace of sin and cos are direct formulas. That is for the (u(t-0)) now just repeat with t-pi. I haven't worked that out but the pi might actually give some nice cancellations somewhere-- i.e. sin(pi)=0 Thanks for the question! Helped me review for my final tomorrow!

[@christopherpayne7650]

all that is wrong nvm ;(

[@nped5054]

@@christopherpayne7650 f(t)=sin⁡(3t)·[u(t-0)-u(t-π)]=sin⁡(3t)·[u(t)-u(t-π)] L{sin⁡(3t)·[u(t)-u(t-π)]}=L{sin⁡(3t)·u(t)}-L{sin⁡(3t)·u(t-π)} sin⁡(3t)·u(t-π) sin⁡(3(t-π))=sin⁡(3t-3π)=sin⁡(3t-π)=-sin⁡(3t) - Trigonometry L{sin⁡(3t)·u(t)}+L{sin⁡(3(t-π))·u(t-π)} 3/(s^2+3^2 )+(e^(-πs) )·3/(s^2+3^2 ) (1+(e^(-πs) ))·3/(s^2+9) This is the process of the task, I would say I calculated the result correct.

[@BEEMOTORS_263-fb2kw]

dude, you dont really have to make applied maths so difficult like in this video. damn!!

[@HorsbonChanda]

Wel explained tutorial really helped

[@innesm5963]

Great Video, cleared up so much before my exam tomorrow. Thank you!

[@hezronmalumo6440]

You are one of the best few ✨🔥

[@danialerfanian6831]

Perfect teaching. Perfect camera view.

[@josephkneeland2579]

This is a nice clear way of solving for the Unit step function. Thank you!

[@BriTheMathGuy]

Glad you enjoyed it!

[@abdirahmanhussein6234]

watchin this b4 midterm, Bri mannnn u helped me a lot keep doin ur stuff

[@justindraheim1911]

is no one going to mention this man is writing backwards. what a legend

[@marcuslawrence7986]

wow. very good explanation. something somebody actually needs. bravo good sir

[@konstantinshterev2860]

bitch ass. wasnt helpful af

[@aalij6610]

شكرا لك على هذا الشرح لو كانت هناك ميزه الترجمه الى اللغه العربيه لكان رائعا

[@albagubrath0098]

you are a savior... thank you so much

[@vishalverma210]

Thanks for explanation. Please also explain in detail about laplace of unit step function .. u(t-1) & t.u(t-1)

[@Collinator02]

Thank you so much, my teacher doesn't speak good english and is honestly crap at teaching. Book with this unit is very unhelpful.

[@Brooklyngilberto]

thank you!! simple and straightforward!!!

[@loganmiert]

You just saved my grade in controls thank you so much!

[@BriTheMathGuy]

Glad I could help!

[@SumitKumar-eh7bd]

Never expected this to be this easy. Thanks man!!

[@BriTheMathGuy]

You bet!

[@youcanspam8107]

You are a lifesaver

[@MUTHU_KRISHNAN_K]

Thank you very much. You have saved my day🙏

[@tanniagonzalez4192]

Oh my gah, these problems were giving me a headache until this video. Bless you sir

[@itsfikree]

Thank you so much sir, very clear explanation 🤩

[@pm2821]

The best start to finish solution I have seen good show thks

[@kingkabester6479]

Yoh!!!!! you saved me ,i was really getting scared.You made this quite easy.Thanks

[@BriTheMathGuy]

No problem 👍

[@kelvinsenteza]

so I'm a little curious; that thing you did before to the piecewise function before applying the Laplace transform; is that decomposition of the function? Saw a similar lot on a math stack exchange and I just want to be sure I got it right

[@jayfromdaa_apk]

Quick and straightforward, great vid

[@youvebeensubbedto8009]

this video made me feel safe ;-; thanks dude

[@dolce_dreemurr]

You are a hero

[@swasticsumansahoo8895]

Great piece of understanding.thank you so much

[@BriTheMathGuy]

You're very welcome. Have a great day!

[@aswinraj9760]

Woow.. Just woow... It was very easy to understand. Thank you

[@sutanukachanda5553]

You made it so easy, you saved my grades thank you!

[@BriTheMathGuy]

Glad it helped!

[@seancox2911]

my textbook does not show any of the steps to get this. They just threw out the step function and how this times the function can get a laplace transformation but for things like the middle part of the piecewise example shown I had no clue how to attack that because I didnt know where this function was coming from and why it was what it was. Thanks for the clarification!

[@hypemanyo]

finally understand how to write unit step function

[@megawar108]

You earned a subscriber ❤️

[@joshuacharlery6060]

BriTheMathGuy is invited to the cookout!!!!

[@valuehunter5544]

salute sir. got right into the meat and potatoes unlike others

[@Lukakuboy92]

final is tomorrow, god bless you brother

[@ulquiorras422]

This guy writing in mirrored for us what a legend

[@roughcatch]

actually, he can write like normal then inverted it later

[@greenxdshadow6635]

you made it so wonderfully easy thank you

[@coltonhiggins5237]

This is much faster and simpler than the way my prof taught it

[@cranky6674]

thanks A LOT

[@DKJhub]

thank you so much! I have a differential equations paper in 2hrs

[@memeduniya567]

thanks a lot😊

[@hazedflare2946]

Just in time for finals! Thank you so much. Do you have a preferred way of viewers to support you? Patreon or paypal etc

[@BriTheMathGuy]

I really appreciate your support simply by watching my videos and commenting :). Have a wonderful day!

[@sunilpandey2426]

Saw this 2 hes before my exam..thanks man..it helped a lot

[@timothychalwe4038]

This is an excellent explanation.

[@HayLaneBF]

Thanks so much!!! You're helping me get that good grade in the final stretch, thanks!!

[@BriTheMathGuy]

very glad to hear it! Best of luck!

[@joshuacharlery6060]

Exceptional Fam!

[@BriTheMathGuy]

Appreciate that!

[@moooadbishtawy6821]

thanks for saving my life

[@BriTheMathGuy]

You got it :)

[@spandansreyanshupadhee]

Way more easier sir , thank you

[@BriTheMathGuy]

Glad it helped!

[@talynjones2552]

Great video helped me out way better than my professor

[@BriTheMathGuy]

Glad it helped!

[@danielhernando377]

thank you man, this really helps

[@BriTheMathGuy]

Very glad to hear it. Have a great day!

[@BriTheMathGuy]

Laplace Transforms! kzbin.info/www/bejne/rKWkZquveb-iiLc

[@habeeba2habi543]

Thankyou man..❤ 🥺

[@finianholland7654]

Love it bro. Thanks for the help

[@BriTheMathGuy]

You got it :)

[@damiangomez1983]

Great video! Greetings from Argentina

[@BriTheMathGuy]

Thanks very much. Have a great day!

[@stephengreenlee9818]

Big help, thank you!!

[@MrBorderlands123]

Excellent video. Thank you!

[@BriTheMathGuy]

You're very welcome. Have a great day!

[@shauryakumar2229]

Really helpful thanks

[@andrewclark9083]

Thanks for explaining it properly!

[@BriTheMathGuy]

Glad it was helpful!

[@דניאלבודילוב]

excellent video, explained better than my professor

[@nirbhaysamrat2180]

Thankyou. I was really confused on how to use the formula as I came across different form of it.

[@BriTheMathGuy]

Very glad to help!

[@deveshwaribhatt]

Thank you so much Sir.. You cleared it out my confusion....

[@BriTheMathGuy]

Happy to help!

[@ahmadaltous5289]

Thank you! You saved me buddy 🙌🏼

[@BriTheMathGuy]

You’re welcome! Have a great day.

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Thank you!

[@BriTheMathGuy]

Welcome!

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i love you man

[@elnarddelaspenas6672]

Thanks man. That's pretty understandable.

[@BriTheMathGuy]

Glad it helped!

[@celinevazquez3299]

THANK YOU

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thank you🫶🏻

[@franciscopovoas8798]

It helped a lot! Thanks bro!

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Allah tutuğunu altın etsin adamsın

[@DeathSorcerer508]

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[@baiyeshaddy4381]

Great video, excellent explanation.