Functional derivatives worksheet

In summary, the conversation is about someone seeking links or resources for practicing with functional derivatives, preferably with solutions provided. They mention having already checked Wikipedia for examples, and are looking for more varied practice problems.
  • #1
HJ Farnsworth
128
1
Greetings,

I want to become more fluent using functional derivatives. Does anyone have a link to sets of problems involving functional derivatives or anything like that (e.g., a worksheet from a class where they were used or something)?

The lengthier the better, and ideally the solutions to the problems would be available as well, so that I could check to make sure that I am using the concepts correctly.

Thanks very much!

-HJ Farnsworth
 
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  • #3
Hi Jorriss, thanks for replying.

You are correct. However, I saw that article when I decided I wanted to learn about functional derivatives, so I sort of know those examples and need some new and different ones to practice.

Thanks again!

-HJ Farnsworth
 

1. What are functional derivatives?

Functional derivatives are a mathematical tool used in functional analysis and calculus of variations. They are used to find the rate of change of a functional with respect to its arguments, similar to how ordinary derivatives are used to find the rate of change of a function with respect to a variable.

2. How are functional derivatives calculated?

Functional derivatives are calculated using the Euler-Lagrange equation, which involves taking the derivative of a functional with respect to its argument and setting it equal to zero. This equation is then solved for the functional derivative.

3. What are some applications of functional derivatives?

Functional derivatives are used in various fields such as physics, engineering, and economics to optimize systems and find solutions to differential equations. They are also used in quantum mechanics to describe the behavior of particles.

4. Can functional derivatives be negative?

Yes, functional derivatives can be negative. This means that the functional is decreasing with respect to its argument. It is important to consider both positive and negative values of functional derivatives to fully understand the behavior of a system.

5. How do functional derivatives differ from ordinary derivatives?

Ordinary derivatives are used to find the rate of change of a function with respect to a variable, while functional derivatives are used to find the rate of change of a functional with respect to its arguments. Additionally, functional derivatives can be functions themselves, while ordinary derivatives are single values.

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