Partial or Regular Derivative for Functional Derivative Stationary Value of 0?

In summary, the conversation involves a question about using a partial derivative or regular derivative to determine the condition for a functional derivative to have a stationary value of 0. The person also provides a helpful resource for the question.
  • #1
delve
34
0
Hi,

I have a question about a functional derivative. When determining the condition that the functional derivative have a stationary value of 0, do I use a partial derivative or a regular derivative? I would really appreciate the help. Thank you!

David
 
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  • #2
delve said:
Hi,

I have a question about a functional derivative. When determining the condition that the functional derivative have a stationary value of 0, do I use a partial derivative or a regular derivative? I would really appreciate the help. Thank you!

David

Could you be a little more specific what the functional is?
Regardless, here is something that you may find helpful:
http://www.math.ucdavis.edu/~hunter/m280_09/ch3.pdf
 
  • #3
Thank you very much! I appreciate it! :D
 

1. What is a functional derivative?

A functional derivative is a mathematical concept used in the field of functional analysis to calculate the rate of change of a functional with respect to its arguments. It is similar to the traditional derivative used in calculus, but is applied to functions that take functions as inputs instead of just variables.

2. How is a functional derivative calculated?

A functional derivative is calculated by taking the limit of a difference quotient, similar to the traditional derivative. However, instead of taking the difference between two values of a function, the difference is taken between two functionals, which are functions that take functions as inputs.

3. What is the significance of functional derivatives in physics?

In physics, functional derivatives are used to describe the behavior of physical systems in terms of functionals, which are more general than traditional functions. This allows for a more comprehensive understanding of complex systems and their behavior.

4. What are some applications of functional derivatives?

Functional derivatives have a wide range of applications in various fields such as physics, engineering, and economics. They are used to solve problems involving optimization, control theory, and differential equations.

5. Are there any limitations to using functional derivatives?

One limitation of functional derivatives is that they can only be applied to functions that are differentiable. This limits their use in some fields, such as computer science, where non-differentiable functions are commonly used. Additionally, functional derivatives can be difficult to calculate for complex systems, requiring advanced mathematical techniques.

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