How to Solve a 4th Order Partial Differential Equation | Vibrating Beam Part 2/2 @FacultyofKhan

Uploaded July 2024 | Updated September 2026, 2 weeks ago

3 years later...this video is the second of two parts on a mini-series discussing the solution to 4th order partial differential equations, using the vibrating beam as an example.

Questions/requests? Let me know in the comments!

Pre-reqs: The previous videos in this playlist - youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD

Lecture Notes: drive.google.com/file/d/1K7tSRaBBAWaUvZsG3D9yqfCHnc5kvvkr/view?usp=sharing

Special thanks to my Patrons:
Patapom
Eugene Bulkin
Andy Johnston
Lina Stritt
Patrick Gibson
Renato Lutz

How to Solve a 4th Order Partial Differential Equation | Vibrating Beam Part 2/2

Wave Equation Solution for a Finite Domain: Standing Waves | Part 2/2

Solving ODEs by the Power Series Solution Method

Isoperimetric Problems | Calculus of Variations

Tensor Calculus: the Derivative of a Tensor

The Faculty of Khans 10,000 subscriber Q and A!

$Introducing Weird Differential Equations: Delay, Fractional, Integro, Stochastic! A brief standalone video that introduces weird types of differential equations, where weird means differential equations that arent conventionally taught unless you get to super specialized areas. Here, they include delay differential equations, integro-differential equations, stochastic differential equations, and fractional differential equations. Questions/requests? Let me know in the comments! Pre-requisites: know what a differential equation is (so basically 1st year undergrad calculus should be more than enough). Lecture Notes: https://drive.google.com/file/d/1zufFLUeUVR6NZqb0MHCQWlnN_6SpOqIb/view?usp=sharing Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan Special thanks to my Patrons for supporting me at the $5 level or higher: Aaron Kaw Cesar Garza Daigo Saito Alvin Barnabas Patapom Damjan Yenyo Pal Lisa Bouchard Gabriel Sommer Eugene Bulkin Rene Gastelumendi Nicholas Chowdhury Borgeth Jose Antonio Sanchez-Migallon$

General Solution to the Wave Equation (via Transport Equation) | (1/2)

4-Momentum and Mass-Energy Equivalence | Special Relativity

The Geodesic Problem on a Plane | Calculus of Variations

Tensor Operations: Contractions, Inner Products, Outer Products