Introduction to Partial Differential Equations: Definitions/Terminology

In this video, I introduce PDEs and the various ways of classifying them.

Questions? Ask in the comments below!

Prereqs: Basic ODEs, calculus (particularly knowledge of partial derivatives/what they are).

[akshayanmuraleetharan]

dam this dude is so good he even figured out why i cared about learning pdes

[UnforsakenXII]

1:32 It is now 12AM. I should technically be studying for my organic chemistry final but this is a good way to procrastinate.

[maomi]

I dishonored my family and failed lots of exams. Your words set me on fire and burned me to the core.😢

[hzkzg]

Your intro is so good that I will watch your preface series first then come back for everything to be crystal clear going on.

[michaelbernthal]

The person who teaches PDEs on you tube on nonhomogeneous differential equations gave a lot of information in a short time.
I did not think I would find anything on the heat equation with an exponentially depletable source input term and the radiation outflow boundary conditions. However I found what I was searching for. Wish there were resources like this 40 years ago.

I'm cramming, yes, but not for an exam. I was out of commission for the first two weeks of the semester, and my professor doesn't give extensions. Ever. So now I have to teach myself the first two weeks' material.

[waynelast]

Very nice review. Best I have seen. However I think you can go one step further, more complication, but if two or more dependent variables exist you can have coupled system of pdes.

[dorianlowden]

Why should I care!!?? 😂 It's exactly why I started watching this video! To cram everything I can for my test...!🙄

[Jordan_]

thanks for the playlist! I havent started this in school yet but we r starting it this year and i wanna get a headstart over summer hehe

[samhenri]

1:21 In the immortal words of Trump: "Wrooong". I am watching your video a month before my term starts to prepare myself for my PDE module. To that end, thank you for making this!

[itsraahul]

Why Should I Care ? Should be the first question every Maths teacher should explain to students at the beginning, that gets students like me curious about the topic, i hate it when teachers just go on teaching without explaining why do we even need it.
hope i had a teacher like you at my college, i suck at maths, thanks for this video sir, and yeah i got exams in 2 days that's why i am here :p can these PDE's be represented Visually ? i am a visual learner so

[zapa]

PDE's are also in mathematical finance, the Black-Scholes equation. This is also a reason why we should care.

[duckyoutube]

My new years goal was to learn Einstein's field equation. Im finally ready. Feels good.

[bijoyroychowdhuryprinon]

excellent explanation..specially the funny part in the middle..keep doing great work..thanks..

[velcro]

Gee was on point about my interest in PDEs

[catprincess]

At 7:24 I think instead of g it should have been the first derivative of f with respect to epsilon. g is being used represent the constant term 1 and y should be represented by the first derivative if f with respect to epsilon.

[Zestyclose-Big]

1:22 me except I've found the playlist way too late and have got probably not even a couple of days

[stephenoni]

what exactly is a variable substitution? thank you for this video! it was very helpful!

[Labroidas]

Good video as usual, but I didn't understand the explanation as to why/ when a PDE is considered hyperbolic. I didn't understand how the variable substitution works after 6:40, I believe I am missing something that is not explicitly said.

[otavakarjalainen]

Great video! I have a question: how do I classify (parabolic, hyperbolic or elliptical) linear 2nd order PDEs in three dimensions, i.e. PDEs with three independent variables? I'm completely stumped...