Deriving the Second Variation | Calculus of Variations

Derivation of the Second Variation of Variational Calculus. This is basically the analog to the second derivative in ordinary calculus, in that it allows you to determine the nature of your function for a particular functional (e.g. whether it's a minimum like a straight line minimizing distance on a plane, maximum etc.).

As you'll see in this video: the derivation is more involved than my derivation for the regular Euler-Lagrange equation. Unlike Euler-Lagrange, the second variation is also much harder to apply as it's not a simple matter of solving a differential equation.

Questions/requests? Let me know in the comments!

Pre-reqs: The previous videos in this playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_

Lecture Notes: https://drive.google.com/file/d/13K1c7vQG1975ISsL-8rWymf0sK--OYV6/view?usp=sharing
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Видео Deriving the Second Variation | Calculus of Variations канала Faculty of Khan