Is this the Correct Solution for Functional Differential Equations?

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  • #1
eljose
492
0
let be the next functional differential equation:

[tex]\delta{F[\phi]}=G[\phi,\partial{\phi}] [/tex]

then its solution would be:

[tex]F[\phi]=\int{D[\phi]G[\phi,\partial{\phi}] [/tex]

would it be correct?..thanks..
 
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  • #2
What does [itex] \delta [/itex] stand for ? The Gâteaux derivative?

Daniel.
 
  • #3
No,no Dextercioiby i meant with delta the functional derivative and D[] the meassure of a functional integral.
 
  • #4
Damn, why wasn't he psychic? Bet he feels bad now.
 

What is functional integration?

Functional integration is a mathematical concept that involves integrating a function over an infinite number of variables. It is commonly used in physics and statistics to study systems with many interacting components.

How is functional integration used in science?

Functional integration is used to solve complex problems that involve multiple variables and interactions. It is commonly used in fields such as quantum mechanics, statistical mechanics, and biology to model and understand complex systems.

What are the benefits of using functional integration?

Functional integration allows scientists to analyze complex systems and make predictions about their behavior. It also provides a powerful tool for solving problems that are difficult or impossible to solve using traditional methods.

What are some limitations of functional integration?

Functional integration can be challenging to perform and often requires advanced mathematical techniques. It also relies on simplifying assumptions and may not accurately reflect the true complexity of a system.

What are some real-world applications of functional integration?

Functional integration has many applications in science, including predicting the behavior of physical systems, analyzing biological networks, and simulating complex systems in computer models. It is also used in economics, finance, and engineering to solve optimization problems.

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