Solving ODEs with Delta functions using Laplace Transforms

Welcome to the final video in our Laplace Transform series! Full playlist for the ODEs course is here: • Laplace Transforms and...
In the previous video we introduced the dirac delta or impulse function and studied many of it's nice properties. In this video we show how to solve ordinary differential equations or ODEs that involve the delta function or a bunch of delta functions. For instance, you could imagine a pendulum being repeatedly hit by a hammer, and model that with delta functions. We study the Laplace Transform of the delta function and show how we can solve these types of ODEs.
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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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[@omraikar8517]

Sir, you have some unique teaching talent. A single play of any of your videos clears the concept. Thanks!!

[@alvinardiansyah8757]

Watch several of your videos about matrices ,vectors, and probabilities, I must admit that you were able to explain it effectively ( I mean most school teacher will only ask you to memorize the formula) but here I am watching over your explanation while you're visualizing it! You're awesome! Keep up the great job!

[@mubashshiruddin3567]

thanks for explaining such difficult and abstract concepts with such beauty and clarity ❤❤

[@user-sq8vu7wr7q]

看完拉普拉斯轉換的播放清單了🎉真的很感謝你出了這麼完整的教程

[@thefrachet]

Really crazy that Math just works out that perfectly in describing real things. 🤯 Absolutely amazing 😍Greetings from Switzerland.

[@duykhanh7746]

This is absolutely stunning! I've never thought this deeply about Laplace transform... Thank you so much for the lecture!

[@yourdad9885]

Super beautiful material with a bright explanation ❤

[@Novak2611]

2:30 there's a missing "minus" in the exponential

[@austinolson6896]

yes I believe it should be x(t) = sin(t+pi)u(t+pi)

[@pratibhasingh4823]

@@austinolson6896 yep... u r right..

[@vijayvarma5501]

​@@austinolson6896yes e^-pi×s/s^2 +1 is mistakenly displayed
But,yes u(t-pi)sin(t-pi) is correct answer
Look into laplace second shift translation theorem

[@goldrush1526]

He has the right answer at the end- just a typo error, the answer is x(t) = sin(t-pi)u(t-pi).

[@stanleytaylor6484]

Great videos. I think the result is e to minus pi s in one derivation, since the delta function pulls the value of e to minus st at t equal pi.

[@user-wu8yq1rb9t]

Minute: 2:00
This video actually have some Physics on it ... Cool
Great video with Great interpretation.
Thank you Professor 💗

[@spacedream195]

So cool explanation. That shows, that it still worths it to do youtube videos, despite the fact there are already so many ragarding to this topic.

[@continnum_radhe-radhe]

This series is awesome..

[@caotinh4503]

hi prof. would it be, e to the (-pi *s) rather than plus there in the first example result?

[@mukkupretski]

You're correct, there's a mistake

[@j.o.5957]

Hard stuff, yet I feel like I have some intuition and some examples, so I should be able to memorize a few patterns and recognize them, then if I apply them at enough problems, I'll eventually get a hang of the calculations.

[@user-gc6we4co4f]

yes you will

[@a.static.kaleidoscope]

thank you master

[@kevinmatagaro7211]

Awesome video.

[@alexanderdrace3585]

For the last example with the reoccurring impulse, could you add some dampening to the system to recreate somewhat of a Newton's cradle? Amazing video!

[@copernicus6420]

As my knowledge on differential equations increased, his beard style progressively improved.

[@NirajMahajan]

Nice one Sir! Would really like to understand your recording setup. I subscribed you when i saw your Conditional Probability videos. I liked them a lot!
I’m really curious about background editing. Is it possible to show us your setup? Eddie Woo has done the same.
Few questions like:
1. Which app for writing you use?
2.Is the background of writing app and your video background same/merged?
3. Like this video using ppt/keynote, again whether background of ppt & your video is same/merged?
I know I’m asking a lot, I also know tremendous efforts goes into research/setup/editing! So kudos to you mate!
Thanks in advance !
A teacher in India 👍🏻

[@NirajMahajan]

Trefor Bazett Thanks a lot!! Wishing you more videos and subscribers 👍🏻

[@andykandolf1948]

what a great channel :-)

[@lindokuhlemthembu3015]

uyayichaza kodwa inyongo

[@augustye3489]

it will be awesome if you watched this series of videos with Gilbert's

[@alimozaffar6884]

Thanks✌✌✌

[@digvijaybokey3585]

It would be e^(-piS) no?

[@oriabnu1]

Delay Compensation using Taylor
Expansion and Hessian Approximation sir I need your video on this topic

[@SHAHHUSSAIN]

You r a grt Sir 😊😊❤❤