Collected Lectures on Calculus of Variations

Gentle introductions #

1. Blog post “The Calculus of Variations” on Bounded Rationality, with intuitive explanations and worked brachistochrone-style examples.

Classic introductory textbooks (PDF) #

1. Gelfand & Fomin – Calculus of Variations (Dover). A standard first text, concise and focused on core theory and mechanics applications.
2. Bruce van Brunt – The Calculus of Variations (Springer Universitext); a bit more modern, with geometry and physics examples, suitable after multivariable calculus and basic analysis.
3. Hunter College notes “The Calculus of Variations” (covers lemmas, Euler–Lagrange, Weierstrass condition, etc.) for a structured, textbook-like PDF. ​

Lecture note sets #

1. Lukas Koch, Lecture notes for Calculus of Variations (Leipzig, 3rd-year course, includes classical theory and direct method, up to modern topics).
2. ​Riccardo Cristoferi, Calculus of Variations Lecture Notes (Carnegie Mellon, classical necessary and sufficient conditions, many examples).
3. Filip Rindler, Introduction to the Modern Calculus of Variations (goes beyond classical theory toward modern functional-analytic treatment).
4. Pisa “Lecture Notes Calculus of Variations A” (introduction, first variation, Euler–Lagrange, with PDE flavor).
5. Long Chen, Classic theory of calculus of variation (focused on Euler–Lagrange, Legendre, Jacobi, Weierstrass conditions, weak vs strong minima). ​