Laplace Transform of a Piecewise Function (Unit Step Function)

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In this video we will take the Laplace Transform of a Piecewise Function - and we will use unit step functions!
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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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[@user-fn1nn1ei8c]

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)?

[@alexanderea99]

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 :)

[@BriTheMathGuy]

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

[@habeeba2habi543]

Thankyou man..❤ 🥺

[@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.

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[@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😂

[@brianhoran9868]

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

[@supertron6039]

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.

[@reeseromero5688]

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

[@BriTheMathGuy]

Glad to help ya out!

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No

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No confusing sketches. Just straight to the point thank you

[@KOKETSOBAKWENAMATHOLE]

You deserve you flowers 🌹. After struggling for hours trying to understand this. Thank you

[@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!

[@JosueBenitez-eg4cz]

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

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[@BriTheMathGuy]

Glad I could help!

[@josephkneeland2579]

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

[@BriTheMathGuy]

Glad you enjoyed it!

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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!

[@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!

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Perfect teaching. Perfect camera view.

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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

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[@BriTheMathGuy]

very glad to hear it! Best of luck!

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You bet!

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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

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i hope u failed ur exam

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[@BriTheMathGuy]

You're very welcome. Have a great day!

[@milesseminario5933]

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

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you made it so wonderfully easy thank you

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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!

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Thanks man!! smooth technique

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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.

[@kedarparab8001]

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

[@BriTheMathGuy]

Glad to help!

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[@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!

[@cranky6674]

thanks A LOT

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thank you man, this really helps

[@BriTheMathGuy]

Very glad to hear it. Have a great day!

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Thank you!

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Big help, thank you!!

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

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[@BriTheMathGuy]

You're very welcome. Thanks for watching and have a nice day!

[@vishalverma210]

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

[@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!

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

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You're very welcome. Have a great day!

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Thanks for explaining it properly!

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Glad it was helpful!

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Glad I could help!

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You’re welcome! Have a great day.

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[@BriTheMathGuy]

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Great video, excellent explanation.

[@DeathSorcerer508]

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[@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.

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

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[@BriTheMathGuy]

Glad you liked it!

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[@BriTheMathGuy]

Really glad to hear it. Have a great day!

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You're welcome!

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

[@BriTheMathGuy]

Happy to help!

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You're welcome!

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[@user-be2hy4yk3b]

excellent video, explained better than my professor

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Thanks very much. Have a great day!

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Thanks a lot buddy!

[@BriTheMathGuy]

You’re very welcome! Have a great day.

[@hypemanyo]

finally understand how to write unit step function

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You're welcome!

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final is tomorrow, god bless you brother