Introducing Weird Differential Equations: Delay, Fractional, Integro, Stochastic!

A brief standalone video that introduces weird types of differential equations, where 'weird' means differential equations that aren't conventionally taught unless you get to super specialized areas. Here, they include delay differential equations, integro-differential equations, stochastic differential equations, and fractional differential equations.

Questions/requests? Let me know in the comments!

Pre-requisites: know what a differential equation is (so basically 1st year undergrad calculus should be more than enough).

Special thanks to my Patrons for supporting me at the $5 level or higher:
Aaron Kaw
Cesar Garza
Daigo Saito
Alvin Barnabas
Patapom
Damjan
Yenyo Pal
Lisa Bouchard
Gabriel Sommer
Eugene Bulkin
Rene Gastelumendi
Nicholas Chowdhury
Borgeth
Jose Antonio Sanchez-Migallon

[aaronkaw]

Wow that was quick, haha. Again very clear and concise, I love it thanks Khan. Worth being a patreon supporter!

[EigenA]

I want my handwriting to look that clean

[smortypi]

I would be ecstatic if you could make further videos on these weird DEs. I'm an EE/Signal Processing undergrad just about to start my upper-level classes at a University. I also have a huge interest in mathematical finance, so naturally I have a huge interest in delay differential equations and stochastic differential equations.
And I thought it was bad when I first glossed through a control systems textbook.
Imagine the punch to the gut when I downloaded an *introductory* book on stochastic DEs and saw the shear breadth of mathematical prerequisites to even begin understanding them. Set theory, partial differential equations (haven't gotten to them yet), rigorous analysis, advanced linear algebra, advanced statistics... a practical undergrad degree's worth of material unto itself. Stuff I'll never be able to touch on doing engineering.

I really appreciate the videos you make, since they let me get a taste of the things I really want to learn about but would otherwise never have the opportunity to do so.

[TB-qkhg]

My ODE teacher had a special section of our coursework. That semester's special topic was DDE because we were in the early part of the pandemic. I really enjoyed that course and he was an amazing instructor.

[bereshyitbara]

clear and concise, deserving MORE subs!

[trevorwynkoop]

Mind blown. The more you learn the more you realize you know very little

[felipegabriel]

What an awesome intro! Do you plan making a series for solving then? Like introducing Riemann-Liouville's and Caputo's integral along with Mitag-Lefler's functions to solve FODEs (Fractional ODEs) or Itō's integral for SODEs (Stochastic ODEs), etc? Would be cool, since there's almost no content available on YouTube on these "weird" topics haha.

[eulefranz]

Interesting. Never heard of delayed DE and fractional DE and that says something! Follow up videos would be very exciting, maybe a few examples and where these weird DE are frequently encountered

[Cat-ircy]

I'm about to take this course next semester, so uh, I hope this makes sense to me by then

[Jehannum]

First.

Was just in the mood for weird differential equations!

[sheeba]

Can you please solve an example using method of steps to solve DDE ?

[thiagoguimaraesmelo]

Hi! What application do you use to make fantastic videos like this? How to make the words appear as in your video?

[rupchandsutradhar]

Can you suggest any book on continuous delay differential equation?

[rafaellisboa]

could you make a sequel? I bet there are many more

[ghoshabir]

What does an antiderivative of a fraction differential look like?? Some sort of "fractional integral" ??

[josh]

Hello. Can you recommend me good reference/textbooks on delay differential equations?

[fahadman]

Sir what software are you using for black board?

[StNick]

I'm curious to see the kinds of phenomena that these DE's can model.

[ahmeds_a]

Hi sir how can i contact to you about a business opportunity, do you have instagram, whatsapp, or email