Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023
Instructors: Alan Edelman, Steven G. Johnson

Description: A “functional” F[u] takes a function u(x) and returns a number (e.g. by integrating), & since functions are perfectly good normed vector spaces we can define derivatives F′ with respect to functions u! This is called “calculus of variations.”

License: Creative Commons BY-NC-SA

[fbf]

Steven Johnson is really a great teacher

[hannahnelson]

Thank you for the best explanation of the Euler Lagrange equation I have ever seen!

[vijitdey]

At 23:24, the first equation that writes df= f(u+du)- f(u)= ..., here I think the dx is missing but it reappears when he puts in the Taylor series expansion-based result.