Variational calculus is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. It has applications in physics, mechanics, geometry, and optimization problems.

Some good textbooks that cover variational calculus include:

Variational Calculus by Jean-Pierre Bourguignon and Hervé Le Dret, which provides a comprehensive introduction to the subject with a geometric approach and many exercises.
Calculus of Variations by I. M. Gelfand and S. V. Fomin, which is a classic text that covers the basic theory and some applications of variational calculus.
Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville, which introduces variational calculus as a tool for machine learning and deep learning models.
Pattern Recognition and Machine Learning by Christopher M. Bishop, which also uses variational calculus for machine learning problems such as Bayesian inference and graphical models.
I hope this helps you learn more about variational calculus.
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