What is meant by functional derivative?

Thread starter saravanan13
Start date Feb 3, 2011
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Derivative Functional Functional derivative

In summary, the functional derivative is a mathematical concept used in functional analysis and calculus of variations to find the extreme values of a functional. It is a generalization of the ordinary derivative, with the key difference being that it measures the change in a functional with respect to one of its underlying functions. This is calculated using the Euler-Lagrange equation, which 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, including classical mechanics, quantum mechanics, thermodynamics, variational problems, optimal control theory, and shape optimization.

Feb 3, 2011

saravanan13

What is meant by functional derivative?
Thanks in well advance.

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Feb 3, 2011

timthereaper

Derivative of a function maybe? =)

Feb 3, 2011

mathwonk

Science Advisor

Homework Helper

we need more context. functional analysis is calculus on infinite dimensional spaces. maybe its a derivative in that context.

Feb 3, 2011

gb7nash

Homework Helper

This?

http://en.wikipedia.org/wiki/Functional_derivative

Seems pretty complex.

Related to What is meant by functional derivative?

1. What is the definition of functional derivative?

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.

2. How is the functional derivative different from the ordinary derivative?

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.

3. What is the purpose of the functional derivative?

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.

4. How is the functional derivative calculated?

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.

5. What are some applications of the functional derivative?

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.