Uploaded July 2017 | Updated September 2026, 2 weeks ago

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In this video, I derive/prove the Euler-Lagrange Equation used to find the function y(x) which makes a functional stationary (i.e. the extremal). Euler-Lagrange comes up in a lot of places, including Mechanics and Relativity. The derivation is performed by introducing a variation in the extremal via a parameter epsilon, and setting the derivative of the functional with respect to epsilon to be zero.

My previous Variational Calculus video was very positively received, so I thought it would be appropriate to continue the series and upload the second video sooner rather than later. Also, you'll notice that the writing here is smaller, but that's because the screen I'm using now is bigger because of my new desktop.

Questions/requests? Let me know in the comments!

Prereqs: First video of my Calculus of Variations playlist: youtube.com/playlist?list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_

Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4MUllbWpMTndFUFk/view?usp=sharing&resourcekey=0-3qCx6OcX7faxNgXy5yGPEg
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan