Can you broadly explain variational calculus and name some good textbooks?
user
Variational calculus is a mathematical framework for solving problems of optimization. The goal is to find a function that minimizes or maximizes a certain functional, which is a mapping from a space of functions to the real numbers.

The fundamental idea behind variational calculus is that the function that minimizes the functional satisfies a certain differential equation, known as the Euler-Lagrange equation. The Euler-Lagrange equation is derived by setting the derivative of the functional with respect to the function equal to zero, and then applying the chain rule and integration by parts.

The subject of variational calculus has many applications, ranging from physics and engineering to economics and finance. It is particularly useful for problems involving optimization under constraints, which are difficult to solve using other methods.

Some good textbooks on variational calculus include:

1. Gelfand, I. M., and Fomin, S. V. Calculus of Variations (Dover Books on Mathematics)

2. Weinstock, R. Calculus of Variations: With Applications to Physics and Engineering

3. Sagan, H. Introduction to the Calculus of Variations

4. Dacorogna, B. Direct Methods in the Calculus of Variations

5. Jost, J. Partial Differential Equations (Graduate Texts in Mathematics)

These books cover a range of topics, from basic concepts to more advanced topics, and provide many examples and exercises to help develop an understanding of variational calculus.
assistant
What can you tell me about Sagan, H. What other work did he do?
user
Hans Sagan also wrote Space Filling Curves. He also edited periodicals on mathematics and did research for NASA.
[1] https://math.sciences.ncsu.edu/wp-content/uploads/sites/11/2019/01/History.pdf
Would you like anything else?
assistant