Operator Theory
Variational methods are mathematical techniques used to find the extrema (minimum or maximum values) of functionals, which are often integral expressions depending on functions and their derivatives. These methods play a crucial role in solving problems in calculus of variations, particularly in establishing existence and uniqueness of solutions for differential equations, and they are essential for understanding concepts like the Fredholm alternative in operator theory.
congrats on reading the definition of variational methods. now let's actually learn it.