Rigorous Differential Equations text

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Discussion Overview

The discussion revolves around recommendations for rigorous texts on differential equations, emphasizing the desire for books that include proofs and theoretical questions, rather than just methods. Participants share their experiences and preferences regarding various texts, aiming to find suitable resources for a deeper understanding of the subject.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses a strong preference for rigorous texts similar to Rudin's style, seeking both theoretical and applied aspects of differential equations.
  • Another participant inquires about the original poster's prior knowledge of differential equations.
  • The original poster mentions having taken an introductory course in Ordinary Differential Equations and desires a more rigorous review.
  • A participant recommends Ross's differential equations book, noting it contains significant theoretical content but may not match Rudin's sophistication.
  • Another participant suggests Teschl's book as a more advanced and rigorous option, highlighting that it focuses less on solving differential equations.
  • Arnol'd's book is mentioned as a valuable resource that connects differential equations with geometry.
  • A participant suggests starting with Coddington's introductory text before moving on to his differential equations book, which they have not yet reviewed.

Areas of Agreement / Disagreement

Participants present multiple competing views on which texts are most suitable, with no consensus reached on a single recommended book. Each suggestion reflects different aspects of rigor and application.

Contextual Notes

Some participants note that certain recommended texts may not fully align with the level of rigor sought by the original poster, indicating a range of sophistication among the suggested books.

SrVishi
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Hello, I am a math major and I was wondering if you guys knew what would be a good rigorous differential equations text. I really like rigor (like Rudin analysis style rigor or whatnot), instead of the typical books that just focus on the method. I want the proofs and everything. I also would like theoretical questions if possible too, and applied as well (I guess it would be hard to find a differential equations text without applications haha). Could anyone tell me if there are any such books? If not, could you at least tell me what your favorite is? I hear Differential Equations with historical notes by Simmons is a good one. Thanks in advance for any response. Sorry if this question is worded weirdly. I'm on mobile in public and can't focus well.
 
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What do you know of differential equations already?
 
I already had an introductory course in Ordinary Differential Equations, though it was kind of a crash course, so I would kind of like to review it, with a more rigorous flavor of course.
 
Well, you probably can't do better than Ross's differential equations: https://www.amazon.com/dp/0471032948/?tag=pfamazon01-20 This is one of my favorite books out there. Be sure to get the 800 page version, since it contains more theoretical stuff.

Now, the book is very good, and contains quite a lot of theory, with of course the existence and uniqueness theorems. But it isn't really comparable to Rudin in terms of sophistication. But I feel that one should understand the material in this book before getting to a more advanced work, since that advanced work will likely take a lot of things for granted that are in such "introductory books".

For a more rigorous and advanced book, I recommend Teschl: https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ which is freely available on his website, but you can buy it too: https://www.amazon.com/dp/0821883283/?tag=pfamazon01-20 This book will not care about solving differential equations though.
 
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You can start with Coddington ( introduction), I am familiar with this one. Then you can try his differential equation book(have not looked at it yet, my understanding is not there yet).
 

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