How to do functional derivatives

  • Context: Graduate 
  • Thread starter Thread starter leroyjenkens
  • Start date Start date
  • Tags Tags
    Derivatives Functional
Click For Summary
SUMMARY

This discussion focuses on the process of calculating functional derivatives, particularly in the context of a homework problem. The participant expresses confusion regarding the application of delta functions as indicated in their notes, seeking a step-by-step explanation. The conversation highlights the importance of understanding when to apply delta functions in functional derivatives, a key concept in variational calculus. Clear guidance on this topic is essential for mastering the subject.

PREREQUISITES
  • Understanding of functional calculus
  • Familiarity with delta functions
  • Basic knowledge of variational principles
  • Experience with mathematical notation and problem-solving
NEXT STEPS
  • Study the principles of functional derivatives in variational calculus
  • Learn about the properties and applications of delta functions
  • Review examples of functional derivatives in physics and mathematics
  • Practice solving problems involving functional derivatives and delta functions
USEFUL FOR

Students in advanced mathematics or physics courses, particularly those dealing with calculus of variations and functional analysis, will benefit from this discussion.

leroyjenkens
Messages
621
Reaction score
49
Here's an example from my homework. I already turned it in, though. I basically just copied what I could from my notes, but I have no idea how this is done.
Could someone explain this to me? I can't find anything intelligible (at least to me) of this stuff on any website. My notes contain parts where the instructor changed certain terms into delta functions, but I'm not sure why, and I don't know when to do that.
So if anyone has the time, could you explain this step by step to me of what this question is looking for? I'll post the picture from my homework.
Thanks.
 

Attachments

  • Untitled.jpg
    Untitled.jpg
    11.6 KB · Views: 453
Physics news on Phys.org
Please post in the homework section.
 

Similar threads

Graduate Is the functional derivative a function or a functional
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K
Graduate The partial derivative of a function that includes step functions
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad How to manipulate functions that are not explicitly given?
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Switching a derivative and a limit is sometimes possible, sometimes not...
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What Are Common Misconceptions About the Dirac Delta Function?
  • · Replies 25 ·
Replies
25
Views
4K
Undergrad Is the derivative of a discontinuity a delta function?
  • · Replies 1 ·
Replies
1
Views
4K
High School How do I invert this exponential function?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Derivatives of Standard Functions
  • · Replies 17 ·
Replies
17
Views
2K
Graduate Derivative of norm of function w.r.t real-part of function
  • · Replies 5 ·
Replies
5
Views
4K