Periodic Functions and the Laplace Transform

We've seen previously in the playlist that Laplace Transforms work great with piecewise functions, functions that have discontinuities in them like the Heaviside or unit step function. In this video we're going to see that it also plays really nicely with periodic functions where f(t+p)=f(t). Indeed, you can always extend a function on an interval to a periodic function on the entire real line and we will have a nice formula from the Laplace Transform to deal with that. This is particularly useful for solving Ordinary Differential Equations (ODE) that have a periodic nonhomogeneity.

****************************************************
Other Course Playlists:

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:

►Want some cool math? Check out my "Cool Math" Series:

****************************************************

*****************************************************

This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[sachinprajapati]

I loved the way he explained the things. He's amazing and made things pretty easier to understand. Please make more videos related to maths.

[sagarchaudhary]

Its underrated channel.
I got each time connected to its content.
Thank you sir.

[thisisbipin]

This guy is literally amazing!!!😊 I like his videos a lot.

[wuyqrbt]

Great ... Beautiful
I just enjoyed, learning is unavoidable!
Thank you so much 💞

[peterfriedman]

I love these videos. So helpful. Wonderful explanations.

[showtime_]

There should be "over s" at the -e^-s term at 7:34

[jeankayembe]

Your channel is a blessing. Keep uploading!! Thank you so much.~~~

[AbhishekKumar-jggq]

Professor you explain it very nicely 👌

[carldan]

fantastic content professor, very helpful but just a question, is there an error in the solution of the last integral? shouldn't it be 1/(1-e^-s)*[-(e^-s)/s -(e^-s)/s^2 +1/s^2]?

[mathematicsmssimplex]

Amazing video. I always enjoy your videos. Your videos Motivate me to create my own

[vikramnagarjuna]

Hi sir, this is Vikram from India I like your videos very much.. animations are good. when will you start vector calculus topics like line integral Green's theorem and so on.

[chathuravimanga]

07:40 Is this final answer allright? I get it but the the -e^(-s) multiplied by a factor 1/s for some reason. (Asking just for clarification)

[wuyqrbt]

Professor ...
I have a question ⁉️ (please if you have time ...)
Minute: 7:40
The final answer is correct?
I checked it, I think we need 1/S for first term.
Thank you

[mariajosechinchillamoran]

Nice! Thanks for your work! I really love your shirt!

[fadiadaghestani]

Cool lecture . I appreciate your efforts professor except of a one small thing:
Infinity does not exist in real life

[TatharNuar]

7:34 Shouldn't the first term in the brackets be over s? I don't know what happened to it from the previous step.

[eleazertham]

Amazing video ❤️and BTW love your shirt..

[_s_l]

Sir, how are we sure that 'sp > 0' when we assuming e to the power -sp is less than 1??

[justiren]

Can i use this method if the problem becomes f(t-p)=f(t)?

[arikaizen]

lets say f(x):[-pi:pi)->R f(x)=x how do you write the equation of the function if if periodical?