Using Laplace Transforms to solve Differential Equations ***full example***

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How can we use the Laplace Transform to solve an Initial Value Problem (IVP) consisting of an ODE together with initial conditions? in this video we do a full walkthrough beginning with the differential equation, converting it to an algebraic equation via the Laplace Transform, solving that algebraic equation, and finally converting back to a solution to the IVP through the Inverse Laplace Transform.

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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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my exam is in a few hours and you are a life saver!!!! thank you!!

lythd
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You just explained how to do this ten times better than my college professor did earlier today. Thank you for the help!

MidwestSirenProductions
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Easier way to solve partial fraction: just decide S to be the roots, for example

S - 1 = A(S + 1) + B(S - 2)
Choose S = -1
-2 = -3B -> B = 2/3
Choose S = 2
1 = 3A -> A = 1/3

Way quicker than solving a linear system of equations

zlatanbrekke
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This is one of the best maths videos ever watches, many thanks.

jamaljaffer
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I am excited after watching this, for no particular reason. Maths just amaze me:) Thank you for this high-quality video series! ( they are so well explained that even a high school student like me can understand!)

cuie
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This was magnitudes easier to understand then the way my professor showed it. Thank you

Mockedarchie
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Done well, really helped me put everything together during these covid self-teaching times.

SB-wkcr
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really concise and clear explanation! thanks a lot buddy! 💙💙💙

allblueandyou
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You are the best math teacher ever💥!!!.

TALCOHOME
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I am so grateful I found your channel tata 😭 God bless you!

ezraitejamile
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Wow, it's like if you're kinda doing exact equations, that's cool, gotta learn this more, thank you again so much for this!

brandonmohammed
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Thank you! Your videos are so helpful while I'm taking DE online!

camillejones
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i dont even know why i show up to class anymore. i learn so much more out of these online videos than i ever will from class

xhydrous
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That clarifies a lot! I might not fail now!

suponjubobu
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Watched all your series videos, they helped a lot thanks so much

OceanageMangoma-wp
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Really saving my engineering ass before my midterm thank you :)

connoratkinson
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Thank You Sir, Very Much Helpful Video.

vedantpratik
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Not bad, but I would like to see the explanation of what is going on under the covers. What was Laplace's thinking when he invented this transform? Same question applies to other integral transforms.

cernejr
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sir post some limit sequense . converge or not. example videos

suhailawm
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You are so polite i wish having happienes in your live

wryanihad