What's a good book for Green's functions?

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The discussion centers on seeking additional resources for studying Green's functions in the context of partial differential equations, specifically while using Asmar's textbook. Participants highlight the importance of Green's functions, also known as impulse response functions in engineering, emphasizing their utility in linear systems. A prior thread is referenced for further insights, and G.F. Roach's book is recommended as a cost-effective option for a deeper understanding of the topic.
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Hello! I'm currently taking a course on partial differential equations, and we're using Asmar's textbook. We've reached Green's functions, and even though Asmar is a great book, I feel like I need a deeper study of the subject. Which book would you recommend to help me better grasp the theory behind Green's functions?
 
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The Green's function is called the impulse response function in engineering, a name which is more descriptive of the idea behind it. It is especially useful in linear systems.
 
Thanks for the link. G.F. Roach's book seems like the way to go. It's not expensive, which is always a good thing.
 
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I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...

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