Best fluid mechanics texts for math majors

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Discussion Overview

The discussion centers around recommendations for fluid mechanics textbooks suitable for a math major with a strong background in advanced mathematics. The focus includes the integration of differential topology into fluid mechanics study.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • A participant seeks suggestions for fluid mechanics resources that align with their advanced mathematical background, including courses in calculus, analysis, and differential geometry.
  • Another participant expresses a specific interest in finding a fluid mechanics book that incorporates differential topology.
  • A suggestion is made for the book "Topological methods in Hydrodynamics" by Arnold and Khesin as a potential resource.
  • A later reply expresses appreciation for the suggestion and highlights a positive view of Arnold's work.

Areas of Agreement / Disagreement

The discussion does not present any clear consensus, as participants are exploring different aspects of fluid mechanics literature without resolving the specific needs or preferences for resources.

Contextual Notes

Participants have not established a definitive list of recommended texts, and the discussion reflects individual preferences and interests rather than a comprehensive guide.

Axiomer
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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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