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saravanan13
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What is meant by functional derivative?
Thanks in well advance.
Thanks in well advance.
The functional derivative is a mathematical concept used in functional analysis and calculus of variations. It is defined as the derivative of a functional with respect to a function.
The functional derivative is a generalization of the ordinary derivative, which is defined for functions of one or more variables. While the ordinary derivative measures the change in a function with respect to one of its variables, the functional derivative measures the change in a functional with respect to one of its underlying functions.
The functional derivative is used in the calculus of variations to find the extreme values of a functional. It allows us to determine which function(s) will make the functional stationary, or have a minimum or maximum value.
The functional derivative is calculated using the Euler-Lagrange equation, which is a necessary condition for a function to be an extreme value of a functional. It involves finding the variation of the functional with respect to the function and setting it equal to zero.
The functional derivative has many applications in physics, engineering, and mathematics. It is used to solve problems in classical mechanics, quantum mechanics, and thermodynamics. It is also used in the study of variational problems, optimal control theory, and shape optimization.