Best fluid mechanics texts for math majors

AI Thread Summary
An undergraduate math major in their third year is preparing for a reading course in fluid mechanics, having completed advanced courses in calculus, analysis, topology, and ordinary and partial differential equations. They are also taking a differential geometry course that includes tensor analysis. The discussion highlights the search for textbooks and online resources suitable for this background, with a specific interest in fluid mechanics literature that incorporates differential topology. A suggested resource is "Topological Methods in Hydrodynamics" by Arnold and Khesin, which aligns with the user's academic focus. The conversation emphasizes the importance of finding high-quality, relevant materials for advanced study in fluid mechanics.
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Hey all. I am an undergraduate math major in my third year who is planning to do a reading course in fluid mechanics next term. I have taken courses in rigorous advanced calculus, real and complex analysis, topology, and intro ODE and PDE. I would be taking a differential geometry course, which covers tensor analysis, concurrently. What are some suggestions for textbooks/online resources for someone of my disposition? Thanks in advance.

Alexander
 
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I'm looking for a fluid mechanics book that is differential topology oriented as well. I'm not having any luck finding such a book however :frown:
 
Perhaps Arnold and Khesin, Topological methods in Hydrodynamics?
 
Jorriss said:
Perhaps Arnold and Khesin, Topological methods in Hydrodynamics?

This is beyond brilliant, thanks! I can always count on Arnold :wink:
 

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