Uploaded January 2018 | Updated September 2026, 2 weeks ago
In this video, I introduce the concept of Laplace Transforms to PDEs. A Laplace Transform is a special integral transform, and when it's applied to a differential equation, it effectively integrates out one of the independent variables to make the differential equation a simpler equation. Once we solve this simpler equation, we can take the inverse Laplace Transform (with the help of tables) and obtain the solution to the original differential equation.
After introducing Laplace Transforms, I apply the method of Laplace Transforms to a simple example involving the heat equation on a semi-infinite domain. After some computation, we end up with a complimentary error function as our solution.
I'm also pleased to announce that after several infuriating months of trying to find a way to display the cursor on my recording, I have finally achieved success. The cursor can be seen as the yellow dot, and I hope that it will make my videos easier to follow. Please be sure to congratulate me on this achievement by writing 'thank mr cursor' in the comments section.
Prerequisites: Basic knowledge of Laplace Transforms from ODEs (though I've tried to give a sufficiently thorough review without getting too thorough) and the first 3 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD
Lecture Notes: drive.google.com/open?id=14uoU3rUmARL7HVTyw9FQBC_pFPNse_eH
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Tom
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
In this video, I introduce the concept of Laplace Transforms to PDEs. A Laplace Transform is a special integral transform, and when it's applied to a differential equation, it effectively integrates out one of the independent variables to make the differential equation a simpler equation. Once we solve this simpler equation, we can take the inverse Laplace Transform (with the help of tables) and obtain the solution to the original differential equation.
After introducing Laplace Transforms, I apply the method of Laplace Transforms to a simple example involving the heat equation on a semi-infinite domain. After some computation, we end up with a complimentary error function as our solution.
I'm also pleased to announce that after several infuriating months of trying to find a way to display the cursor on my recording, I have finally achieved success. The cursor can be seen as the yellow dot, and I hope that it will make my videos easier to follow. Please be sure to congratulate me on this achievement by writing 'thank mr cursor' in the comments section.
Prerequisites: Basic knowledge of Laplace Transforms from ODEs (though I've tried to give a sufficiently thorough review without getting too thorough) and the first 3 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD
Lecture Notes: drive.google.com/open?id=14uoU3rUmARL7HVTyw9FQBC_pFPNse_eH
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Tom
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
