Green Functions: A physicist's Intro to Math Methods

In summary, the individual is a physics student looking for resources on Green functions at a level that does not require a significant knowledge of integral equations and functional analysis. Suggestions were given for a website and a book to check out, as well as a recommendation to visit a library. The Roach and Habermans' books were also mentioned.
  • #1
will.c
375
1
Not sure if this is the best place, but it's also my first post, so meta-answers about where I'm supposed to put this business are welcome too.

I'm a physics student, and I'm interested in learning about Green functions, but I sold back the Boas book that I used for my math methods class (we didn't cover the topic), and that's about the level that I'm looking for; is there a free resource that explains the method in a way that I don't need a huge knowledge of integral equations and functional analysis to comprehend, or at the other end, a book that brings all those topics together so that a physicist can understand it?

Thanks,
Will
 
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  • #2
No help?
 
  • #3
You could try [/URL] to begin with, including the external links and book references at the bottom.

Furthermore, a search on Google returns http://books.google.nl/books?id=edTngEuzXaoC&dq=greens+functions&pg=PP1&ots=bYdfU5doDf&sig=v_tyaPwJ-VArMLGE8mB8CwCnvyI&hl=nl&prev=http://www.google.nl/search?q=greens+functions&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&sa=X&oi=print&ct=title&cad=one-book-with-thumbnail#PPA2,M1 which looks promising to me, but I don't know if it is what you want.

You could also go to your library and see what they have on the subject, then you can hold the book and look inside it.
 
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  • #4
Well, I've done all that, but everything I've come to is either at a graduate level, or advanced undergrad, but for math majors. The Roach book is probably the best on the subject for undergrads, from what I've seen, but it put me to sleep. =(
 

What is a green function?

A green function is a mathematical concept used to solve differential equations in physics and engineering. It represents the response of a system to a delta function input, and can be used to find the solution to a general input by convolving it with the input function.

How are green functions used in physics?

Green functions are used in physics to solve boundary value problems, such as those found in electrostatics, heat transfer, and quantum mechanics. They are also used in scattering theory to calculate the response of a system to an external force or potential.

What are the properties of a green function?

A green function must be symmetric, satisfy the boundary conditions of the problem, and have a singularity at the point where the delta function is located. It also has the property of linearity, meaning that the solution to a linear differential equation can be obtained by summing the responses to each component of the input.

How are green functions related to Fourier transforms?

Green functions and Fourier transforms are closely related, as they both represent the decomposition of a function into its constituent parts. Fourier transforms are used to decompose a function into its frequency components, while green functions are used to decompose a function into its spatial components.

What are the applications of green functions?

Green functions have many applications in physics and engineering, including in electromagnetism, fluid dynamics, solid mechanics, and quantum mechanics. They are also used in image and signal processing, as well as in financial mathematics and statistics.

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