When the Netflix series The Three Body Problem (based on the excellent trilogy by Cixin Liu) came out last year (2024), there was a lot of talk about the physics problem that gave the book its name.
Since I am the spiritual leader of my group when it comes to mathematics 😇, I decided to give a presentation on classical mechanics to my colleagues. I showed them how to derive the Euler-Lagrange equation and how to use it to solve some variational problems.
The book I used as a reference was Calculus of Variations (1952) by Robert Weinstock. This is undoubtedly one of my favorite math books ever. It starts with a general introduction covering prerequisites and basics, and jumps right into applications, starting with basic iso-perimetric problems, through famous problems like the brachistrochrone, the principle of least action, all the way to quantum mechanics, including the original derivation of the Schrödinger equation.
I really love books from this period, the typography is just beautiful. The copy I have is a reprint, but a beautifully done one, with the original design, and good quality, yellowish paper that gives the book a vintage feel.
P.S. For the more mathematically inclined, I can also recommend the book by Gelfand and Fomin (1969). I have a Dover English edition. Both books are also available online.
