Request for tutorial on funtional derivatives

In summary, if you're struggling to understand functional derivatives, I recommend checking out these resources for a step by step guide on how to evaluate them. They provide clear explanations and examples that can help you make sense of this complex topic.
  • #1
leroyjenkens
616
49
Would anyone here know where I could find some kind of tutorial that goes step by step of how to evaluate functional derivatives? I'm looking over my notes, trying to make sense of this functional derivatives stuff the teacher did in class, and it makes no sense at all. I'm not even in the realm of beginning to understand what's going on. There's dx's and deltas and partial derivative symbols flying around all over the place like some kind of mathematical Jackson Pollock painting.
This was never covered in any math class I've had, the physics teacher just starts throwing it in and quickly going over all these strange manipulations you can do with it, like it's second-nature to us or something.
And this is something I can't seem to find anything about online. Usually I can find tutorials on youtube or something, but nothing I type in regarding this stuff brings up any relevant results that I can understand.
 
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  • #2
I recommend taking a look at the following resources: 1. Khan Academy: Khan Academy has an excellent tutorial on the basics of functional derivatives, including a step by step guide to evaluating them. 2. MIT OpenCourseWare: MIT OpenCourseWare also has a great course on functional derivatives, which covers the basics as well as more advanced topics. 3. Wolfram MathWorld: Wolfram MathWorld provides a comprehensive overview of functional derivatives, including examples and explanations of how to evaluate them. 4. YouTube Tutorials: There are several excellent YouTube tutorials on functional derivatives that provide a detailed explanation of how to evaluate them.
 

1. What are functional derivatives?

Functional derivatives are a mathematical concept used in the fields of physics, engineering, and mathematics. They are similar to ordinary derivatives, but instead of being defined on functions of a single variable, they are defined on functions of multiple variables. In other words, functional derivatives are derivatives with respect to functions.

2. Why are functional derivatives important?

Functional derivatives are important because they allow us to describe how a functional (a function that takes in a function as its input) changes with respect to its input function. This is useful in many areas of science and engineering, such as optimization, control theory, and quantum mechanics.

3. How do functional derivatives differ from ordinary derivatives?

Functional derivatives differ from ordinary derivatives in that they are defined on functions of multiple variables, rather than just one variable. Additionally, functional derivatives are defined with respect to an entire function, rather than just a single point on a function.

4. How are functional derivatives calculated?

The calculation of functional derivatives depends on the specific functional being considered. In general, functional derivatives can be calculated by using the Euler-Lagrange equation, which relates the functional derivative to the partial derivatives of the function being differentiated. However, more complex methods may be required for certain types of functionals.

5. What are some applications of functional derivatives?

Functional derivatives have a wide range of applications in various fields of science and engineering. Some common applications include optimization problems, where the goal is to find the function that minimizes or maximizes a given functional, and control theory, where functional derivatives are used to describe how a system evolves over time. Functional derivatives are also used in quantum mechanics to describe the dynamics of a quantum system.

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