Uploaded July 2017 | Updated September 2026, 2 weeks ago
Hey what's up guys, Scarce here, and today we have a DOUBLE UPLOAD! So much drama to get through (Jake Paul+Tessa Brooks+Some FaZe guy+Keemstar+Pewdiepie etc etc), so let's get started.
Sorry about that lol. Anyway, in this video, I derive the general solution to the wave equation by solving two transport equations. I begin by deriving the general solution to a homogeneous first-order PDE with constant coefficients (equation 2 in the video). I then use the general solution to that first order PDE to derive the general solution to the wave equation. Ultimately, I determine that the general solution to the wave equation consists of the addition of two functions, which we will later see represent forward travelling and backward travelling waves.
ERRATA: At 4:38, I should have said du/dy instead of du/dt.
Questions/requests? Let me know in the comments!
Prereqs: First two videos in this playlist and the most recent video (i.e. video #9 in the playlist) will help: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4TEF0YVF4XzB4b2M/view?usp=sharing&resourcekey=0-RVC70B4WKFU_qa_peMpgvw
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
Jennifer Helfman
Jacob Soares
Hey what's up guys, Scarce here, and today we have a DOUBLE UPLOAD! So much drama to get through (Jake Paul+Tessa Brooks+Some FaZe guy+Keemstar+Pewdiepie etc etc), so let's get started.
Sorry about that lol. Anyway, in this video, I derive the general solution to the wave equation by solving two transport equations. I begin by deriving the general solution to a homogeneous first-order PDE with constant coefficients (equation 2 in the video). I then use the general solution to that first order PDE to derive the general solution to the wave equation. Ultimately, I determine that the general solution to the wave equation consists of the addition of two functions, which we will later see represent forward travelling and backward travelling waves.
ERRATA: At 4:38, I should have said du/dy instead of du/dt.
Questions/requests? Let me know in the comments!
Prereqs: First two videos in this playlist and the most recent video (i.e. video #9 in the playlist) will help: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4TEF0YVF4XzB4b2M/view?usp=sharing&resourcekey=0-RVC70B4WKFU_qa_peMpgvw
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
Jennifer Helfman
Jacob Soares
