Solving ODEs with Delta functions using Laplace Transforms

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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[alvinardiansyah]

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!

[mubashshiruddin]

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

[duykhanh]

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

[Novak]

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

[wuyqrbt]

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

[spacedream]

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.

[j.o.]

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.

[caotinh]

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

[omraikar]

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

[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 👍🏻

[copernicus]

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

[oriabnu]

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

[thefrachet]

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

[yourdad]

Super beautiful material with a bright explanation ❤

[stanleytaylor]

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.

[alexanderdrace]

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!

[augustye]

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