Laplace Transform: The Derivative Theorem and One Example

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In this video I show the justification for the derivative theorem for the Laplace Transform. This is a useful technique so it is worth understanding the derivation.
I also look at one example use the derivative theorem for the Laplace Transform at the end.
This topic will often be encountered in a differential equations course.

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You make every subject so easy to understand. If I am passing the differential equation it is because of you.Thank you so much. You are awesome.

dilekbond
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I really appreciate you making these videos, they are a real life safer.

sinethakmeemana
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Patrick literally pulls down his pants and SHITS ON every other math professor out there.

davidontiveroz
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You are the teacher i need but dont deserve ! *Batman theme song in background*

saket
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you seem to allways know what i am studying to upload a video just in time :)

mateope
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Any chance you can do the Integral Theorem of Laplace as well?

manslayerpupil
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Thank you sir...you made my nightmare become a sweet dream.RESPECT!!

karabotshehla
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Just wanted to mention at 4:17 I think that you made a mistake saying that you are using the product rule. I didn't see the product rule used there. Great video still.

jaraddemarco
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Hey Patrick; could you tell me why you took the partial derivative inside the integral?

Soumil-f
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Thanks for the proof but wouldn't you mind explaining the definition in the proof before using l

ahmedhammad
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Sir, what if the exponent of t is 2, do i just take the second derivative of the function? thank you Sir :)

Sy-qidh
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Hi i got a question, what if t becomes t^2 (t square)

vandersex
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I cant understand the integration part how did -t came?

karnikkalani
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a differential equation in markov modeling 
P’1(t)= P1(t)(1-(a+b))dt + P2(t)cdt + P3(t)edt
P’2(t)= P1(t)adt +  P2(t)(1-(c+d))dt + P3(t)fdt
P’3(t)= P1(t)bdt + P3(t)d dt + P2(t)(1-(e+f))dt
dt=0

P’2(t)=P1(t)a+ P2(t)(1-(c+d))+P3(t)f
P’3(t)=P1(t)b+P3(t)d+ P2(t)(1-(e+f)
  
using laplace transform...

  how can you solve this one.. pls help me! thank you!

junepetermicoligason
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you are Always Awsome! could you upload please a vedeo about  ''Unit step function'' thanks

Adkorane
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patrick will u marry me im a str8 dude!

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