Wave Equation

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES...
Instructor: Gilbert Strang
The wave equation shows how waves move along the x axis, starting from a given wave shape and its velocity. There can be fixed endpoints as with a violin string.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@jrrustad]

So amazing to be able to see Prof. Strang give a lecture. His books on linear algebra and applied math were extremely enlightening to me when I was just getting into computational modeling in the mid 1980s. In those days I lived on a diet of Feynman and Strang, but only through writing. Now you can actually watch them! What a great world we live in.

[@jonahansen]

I love this guy. What a great teacher. I'm glad he's doing this stuff and not retiring. He's a legend!

[@61rmd1]

Prof. Strang, and Prof Balakhrishnan are by far the best teachers i've ever listened. Two giants!

[@crystalc1ear]

If the delta function confuses you, I guess a very simplified way to think about it is a function called "BOOM" where you hear a boom when the input is 0. Let c=10 meters/second. If you are standing at x=0, you hear the boom immediately If you are standing at x=20, then it takes 2 seconds to hear the boom (you hear the boom at t=2). Similar thing happens at x=-20 (this is the leftward traveling wave). The farther you are from x=0, the longer it takes to hear the boom.

[@andrewarmenta2700]

Buy if we move our cellular structure from one place to another... Is telepathy real...

[@frun]

Physics is always dealing with approximations, therefore as it confuses me I still fine.

[@bd_harold7752]

These are invaluable lectures which should be passed for generations to come

[@gustavnordin8690]

Thank you Prof. Strang. I really appreciated that. Will look at your other lectures.

[@marverickbin]

i remember when i was modeling guitar string positions and sound with 1d wave equation, with initial conditions as a ramp, simulating the pick on the string, and strings always at 0 on edges. really cool.

[@sanazgholitabar2599]

i almost finish my master with his videos ;)

[@georgesadler7830]

The wave equation is another classic equation of partial differential equation. This equation has many applications in physics and engineering.

[@leilikheirkhah6203]

Such an amazing professor who teach all around the world, just I am imagining how his grandchild proud of him, cute grandpa !!!

[@AhmedSALAH-bb7un]

I owe this man alot, Thank you professor!!

[@saifusmani5476]

Really this lecture is amazing.. I had never watched this type of video. Nice

[@КлинтИствуд-ъ3и]

Thank you very much! Your lectures is definitely one of the most valuable gifts live gave me.

[@hypatiakovalevskayasklodow9195]

Клинт Иствуд хелоу!

[@szymonaugustynowicz630]

nice :)

[@hypatiakovalevskayasklodow9195]

I wish people who teach to groups that are more to theoretical mathematics side would still keep all the physics examples in I'm all for hard core math, but let us not forget it all had inspiration in nature in the first place

[@gsuth20202]

modern physics and modern math are two sides of the same coin so idk why we dont join them as an area of knowledge. you can still have the complexities of both without acting like the other doesnt exist

[@Pranav_Bhamidipati]

@@gsuth20202 It'll get tedious to learn, and difficult to teach introductory courses. The splitting of subjects is just as logical as splitting a subject into multiple courses or subtopics. You learn the basics first, without requiring much pre-requisites or being hosed down by the breadth of content you cover. When you have sufficient depth in both fields (typically, a semester is sufficient), you can start learning it in a combined way - by analysing problems and particular phenomena with the full bashy force - not leaving out any details. It is the most efficient way to do both.

[@hypatiakovalevskayasklodow9195]

@@gsuth20202I am not even talking about teaching physics - just giving more examples like this, from physics The people who taught PDEs to me would basically give no examples. “here’s the wave equation” or “here’s the Dirac function” without any descriptive example of connecting it to the real world

[@pablomendez3768]

Excelente video Profesor Strang, continue dando sus valiosos aportes. muchas gracias por compartir sus conocimientos. Saludos desde venezuela!

[@andrewarmenta2700]

...and at times we learn different languages, however physics are universal

[@iotdeveloper]

He is not a genius but much much more than a genius because he produces genius.

[@muneebasghar8042]

6:14 "that's a cool solution"

[@frun]

This is what I was looking for. I can see, those are two different equations, now :P

[@jinkilove8020]

awesome series it was really helpful

[@not_amanullah]

Thanks ❤️🤍

[@qinisodlamini1139]

This guy is amazing

[@szymonaugustynowicz630]

agree

[@dhanraaj]

you are the boss. thankyou sir

[@josechemist]

Why is called a hyperbolic equation? Is there solutions using hyperbolic functions compared to the trigonometric functions used in spherical coordinates?

[@impastyle]

brilliant

[@cosmasmwamwembe3409]

you're the best! Thanks

[@paulg444]

he is good!

[@gowatamkumar5909]

Hello sir I m from India I'm student of b.sc. my favourite subject is physics & I m fan of Einstein & Newtown & Hawking

[@colin2209]

does anyone know where is the video about the separation of variables?

[@bhaskarMridul]

Yes

[@dwaipayanroychowdhury]

Hello, does anyone of you has the full playlist of the course? If you do, can you please share it? I searched but couldn't find, need some help.

[@mitocw]

KZbin playlist: kzbin.info/aero/PLUl4u3cNGP63oTpyxCMLKt_JmB0WtSZfG. More course info on MIT OpenCourseWare at: ocw.mit.edu/RES-18-009F15. Best wishes on your studies!

[@pavansharma99]

does he mean heat = EMR?

[@sontungnguyen5506]

Love from VietNam

[@gopalkrishnamukerjea4319]

🙏

[@sebah1991]

As much as I love Gilbert Strang and his Linear Algebra course, this is not a good lecture. I have no idea how someone who has never seen the wave equation could get anything useful from this lecture. You cannot just introduce the wave equation, d'alambert's approach (for IVP and IVBP) and fouriers approach in a 15 minute lecture. These topics are multiple chapters in any PDE textbook. I was watching this video as a review and even though I have already studied these topics, it was very hard to follow. Maybe Prof. Strang should do a few more videos on this topic.

[@devnull256]

I don't think this is meant as standalone lecture to teach wave and heat equations. It perhaps thought as complimentary theoretical recap for MATLAB part of the course. Example of solution in 2D kzbin.info/www/bejne/maK9Z5lsbaeSnMk

[@jeffcandy2479]

I think its an excellent intuitive explanation of the difference between heat/diffusion and wave equations.

[@marcionele1164]

Thanks Prof. Strang! In these classes, I revived much of my undergrad math courses. Your passion and clarity were very stimulant and it was a pleasant trip. Best wishes.

[@MightyForces]

Rip miss u professor gilbert

[@flameon8185]

I can clearly see u winking - DRAX

[@omarelabyad2010]

They should make a Nobel prize for teaching just so they can award it to Prof. Gilbert.