Calculus Of Variations (Noun)
Meaning
The calculus of maxima and minima of definite integrals.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The calculus of variations is a field of mathematics that deals with the problem of finding the extremal functions that can render the given functionals to the minimum or maximum possible values.
- The Euler-Lagrange equation is a fundamental concept in the calculus of variations, used to determine the functions that maximize or minimize the definite integral.
- The calculus of variations has numerous applications in physics, particularly in classical mechanics and quantum field theory, where it is used to determine the optimal path or configuration that minimizes or maximizes the energy or action.
- One of the earliest problems solved using the calculus of variations was the brachistochrone problem, which involved finding the curve along which a particle would slide in the shortest time.
- The calculus of variations can also be applied to optimize systems and find the maximum or minimum values of complex systems in economics, biology, and engineering.