Laplace Transform and Piecewise or Discontinuous Functions

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This video deals particularly with how the Laplace Transform works with piecewise functions, a type of discontinuous functions. The easiest example of which is the step function or heaviside function and we use that example to deal with the more complicated cases. Indeed, one of the big advantages of the Laplace Transform is that it deals with discontinuous functions so well converting them into a continuous function over in "Laplaceland" (a magical place). We will use these formulas as well to deal with inverse laplace transforms.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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Your cadence and inflection is one of the clearest and easiest to understand voices on youtube. Thank you for all of the help.

jayfeatherftw
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I'm not sure why, but the pacing of your explanations is absolutely perfect. As in the speed at which you explain, is like, on my and many others "wavelengths". If only my differential equations professor taught like you did.

snp
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I can sense that you love what you, re doing hence thats why you explain things so clearly, with patience, you are what we call the perfect teacher

philanisithole
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Please do make a series on complex really hard to understand & even harder to make sense and visualise

jjqerfcvddv
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Thank you Professor. You have such a gift of explaining complicated math with such simplicity. You are a gem. Wish I was your student in person, but I am your student here for sure. Blessings to you and your family Sir.

zenithbhurtel
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I had to watch it like 8 times but I finally got it! Thanks a bunch!

crazygury
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I am just now learning laplace transform.

pinklady
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7:34 the defention of how he converted the piece wise function into a simple step function is just mind blowing, great work again sir....

mohamedirshaathm
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Thank you for all your hard work! Helped me greatly. And I love the speed at which you go. You're the only youtube tutor that I find hard to keep up with at 1.5x!!

abhijeetkochhar
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Thank you Trefor! You have the clearest explanation so far on this subject.. Hope you upload more videos on discontinuities in laplace transform.

BlueCollarEngineer
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This video should go viral!! For real. Thank you so much. Your channel is very helpful!!!

jeankayembe
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This was so thorough and helpful! Thank you!

Suzytnwl
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Hello Trefor, i am Mishu from Bangladesh and i watch your video regularly. It helps me enormously to understand the things. You explain nicely. I have a request, can you please make a video about convergence and uniform convergence with some examples? Thanks!

mishudhar
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Hey admire your effort in helping visualise quality content 👍👍👍👌👌👌👌

jjqerfcvddv
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Woah, he called me a mathematician. I'm somebody now. 😎

ChrisDoll
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Which part of Canada are you from, my dude? You remind me of a good friend from Edmonton. Oh, also, thanks for the explanation of the piecewise transform. This summer class is killing me.

jogey
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Is it possible to get the Laplace transform of Step function multiplied by derivative ? L{ U(t-a) F'(t) }

ibrahimeltaleb
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Hello sir, I had a question;
what if the function gives 25 where 0<=x<=2 and gives 20 where x<2. I couldn't understand what could i do when the function have two inclusion point.

alperenyogun
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5:08 doesnt u(t-a) need to be added on left hand side of = sign too?

bandekarameya
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What if the function is of a higher order? then the trick of +a -a won't work as well. What to do in this case?

alexdima