Uploaded July 2017 | Updated September 2026, 3 weeks ago
In this video, I introduce the subject of Variational Calculus/Calculus of Variations. I describe the purpose of Variational Calculus and give some examples of problems which may be solved using techniques from Calculus of Variations.
Specifically, Calculus of Variations seeks to find a function y = f(x) which makes a functional stationary. Note: a functional is a function of functions, or a map which converts a function to a real number, kind of like how the time functional T converts a particular function/particle path to a real value of time. I would have included the Euler-Lagrange proof but it would have likely made the video over 15 minutes, which is a little too long for us.
Questions/requests? Let me know in the comments!
Prerequisites: Not many, just know Calculus 1 (obviously). For later videos, a background in ODEs will be needed, though you don't need to be an expert in them since I'll walk you through :)
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4M2h3MmdaMi1xTFU/view?usp=sharing&resourcekey=0-5xTGxdYKniT-pdb0d427NQ
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
In this video, I introduce the subject of Variational Calculus/Calculus of Variations. I describe the purpose of Variational Calculus and give some examples of problems which may be solved using techniques from Calculus of Variations.
Specifically, Calculus of Variations seeks to find a function y = f(x) which makes a functional stationary. Note: a functional is a function of functions, or a map which converts a function to a real number, kind of like how the time functional T converts a particular function/particle path to a real value of time. I would have included the Euler-Lagrange proof but it would have likely made the video over 15 minutes, which is a little too long for us.
Questions/requests? Let me know in the comments!
Prerequisites: Not many, just know Calculus 1 (obviously). For later videos, a background in ODEs will be needed, though you don't need to be an expert in them since I'll walk you through :)
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4M2h3MmdaMi1xTFU/view?usp=sharing&resourcekey=0-5xTGxdYKniT-pdb0d427NQ
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
