Inverse Laplace Transform Example using Partial Fractions

In this video in my series on Laplace Transforms, we practice compute Inverse Laplace Transforms. In this specific example, the rational function isn't of the form where we can use Inverse Laplace Transforms directly so we use Partial Fractions to decompose it into a more straight forward format. Specially this Partial Fraction Decomposition involves repeated linear factors. Finally we use the Laplace Transform table of known functions together with the translation property to compute the final answer.

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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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[chrisperez]

You honestly made this a whole lot easier, I hadn't done partial fractions since calc 2. Really made it easy to understand, thank you !

[patricklehmann]

Your video series on the Laplace transform is just brilliant 👍🏼👍🏼

[pravii]

even with number of poles > 3, this approach is much faster. Thank you so much.

[SHAHHUSSAIN]

What a grt lvl of confidence, concept as well as good body language, comunication ....I hats off 🎓for you SIR with MASSIVE RESPECT❤!!!

[chelseaker]

I started watching your videos Freshman year in Calc 1 at UC. (I had Dr. Knoll) So funny to stumble upon your video when I was trying to refresh on this topic! Awesome to see how your channel has grown! Great videos thanks!

[spencerfrancoeur]

I was taught a cool trick to solve A at 4:23, I think its called the method of predetermined coefficients? I think it only works for the highest power coefficient. So in this case, you would have

s^2 + 9s + 2 = A(s -1)(s+3) + B(s+3) + C(s-1)^2

So, A would have s^2 and C would have s^2 and the coefficient on the left hand side for s^2 is 1

Therefore, we would have

S^2 = As^2 + Cs^2
Then,
1 = A + C

Since we easily solved for C = -1
1 = A -1
Therefore,
A = 2

This method comes in handy for more difficult equations and saves time when the rule applies.

[jkuebler]

Ive watched dozens of videos on Laplace and inverse Laplace, this is the first video that really made me click and have that Aha! moment. Thank you. You demonstrated the material very well. Excited to watch your other videos.

[ayaadel]

thank you so much these videos are so helpful, and the most special thing a bout your videos is that you explain How to think in every step and where did they come from, thanks.

[Meridiu]

learned this in less than five minutes. you are awesome.

[j.o.]

Was actually able to hang on to this one a bit, nice

[fidelcertuche]

Thank you for this simple but masterly explanation!!!!

[MayankJawadekar]

Hello sir
I am from India. And I am preparing for GATE Exam. This video was really helpful. Thanks a lot sir

[CycleTheDark]

Damn u r better than my college professors... They didn't raise the bar too high tho 😂. I'll make sure to subscribe u are excellent at explaining things. Thanks

[vivaldiantonio]

Hi Trefor ! I watched your whole linear algebra series last year but when i saw that you only got like 30k sub i thinked that this channel was dead. But suprisingly, you constantly upload your video despite of little sub. Thanks for all your teaching. God bless you, Jesus protect from Virus ! Love you.

[tusharsoniiit-kanpur]

Your way of teaching is awesome!!.. More power to you sir

[jdantonio]

Thank for your video. I need that shirt!

[estebansanchezsevilla]

Thanks for the video! Highly appreciated :)

[zzzluke]

Hi, do you think you can do a video on the sequence for laplace transform and also inverse transform? like should we scale first or translate first, how to decide the power etc. Thank you so much for the wonderful videos.

[Kimmy-hogh]

Say the denominator of our transfer function was s(s^2+1), would we have A/s + B/s^2+1 + C/s^2+1? Or would there only be one s^2+1 term?

[rickykris]

oh l like your shirt too !!!
l'm kinda busy recently, l promise l'll watch all videos l missed in the past few months