Thank you!caz said:For calculus of variations check out
https://www.amazon.com/dp/B00JKIJKAE/?tag=pfamazon01-20
For green‘s functions
https://www.amazon.com/dp/0486797961/?tag=pfamazon01-20
Calculus of Variations is a branch of mathematics that deals with finding the optimal solution to a given functional. It is important because it allows us to solve problems in physics, engineering, and economics by minimizing or maximizing a certain quantity.
Sturm Liouville Theory is a mathematical theory that deals with the properties of differential equations. It is closely related to Calculus of Variations because it provides a framework for solving boundary value problems, which are often encountered in Calculus of Variations.
A good textbook for learning Calculus of Variations and Sturm Liouville Theory should have clear explanations of concepts, a variety of examples and practice problems, and a comprehensive coverage of the subject matter. It should also be written in a way that is accessible to students at various levels of mathematical background.
It is recommended to have a strong foundation in calculus, linear algebra, and ordinary differential equations before studying Calculus of Variations and Sturm Liouville Theory. Some knowledge of complex analysis and functional analysis may also be helpful.
Some popular textbooks for learning Calculus of Variations and Sturm Liouville Theory include "Calculus of Variations" by I.M. Gelfand and S.V. Fomin, "The Calculus of Variations" by Bruce van Brunt, and "Sturm-Liouville Theory" by G. Teschl. However, the best textbook for you may depend on your specific learning style and background, so it is recommended to do some research and read reviews before choosing a textbook.