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Calculus of Variations is the study of maximizing or minimizing functionals, which are mappings from a set of functions to real numbers. It involves finding functions that make these functionals attain extreme values, often by solving Euler-Lagrange equations. This field has applications in physics, engineering, economics, and other areas where optimal solutions are sought. In the hierarchy of Science/Mathematics/Optimization Theory, Calculus of Variations is a branch that deals with optimization problems involving functions and functional relationships, providing a mathematical framework for understanding and solving such problems.