Uploaded March 2025 | Updated September 2026, 1 week ago
Separation of Variables
Here is one of the most important techniques for solving partial differential equations: Separation of Variables. We illustrate this by solving the heat equation on a finite interval with zero boundary conditions. It is a technique that is general enough that it allows us to solve other kinds of PDE as well. This leads us through the world of eigenvalues and eigenfunctions and boundary-value problems and ultimately leads us to Fourier sine series, which is a way of expressing a function in terms of sine waves.
Boundary Value Problems: youtu.be/_jE0rqYyupo
How to finish solving this problem: youtu.be/_Wtuek3oiGc
Fourier series playlist:
youtube.com/playlist?list=PLJb1qAQIrmmCH7I01p-8p3z2CIenW6hwe
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
Separation of Variables
Here is one of the most important techniques for solving partial differential equations: Separation of Variables. We illustrate this by solving the heat equation on a finite interval with zero boundary conditions. It is a technique that is general enough that it allows us to solve other kinds of PDE as well. This leads us through the world of eigenvalues and eigenfunctions and boundary-value problems and ultimately leads us to Fourier sine series, which is a way of expressing a function in terms of sine waves.
Boundary Value Problems: youtu.be/_jE0rqYyupo
How to finish solving this problem: youtu.be/_Wtuek3oiGc
Fourier series playlist:
youtube.com/playlist?list=PLJb1qAQIrmmCH7I01p-8p3z2CIenW6hwe
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
