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khemix
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Want a good diffy book. Two names I hear are Arnold and Hirsch. Are they good?
Vid said:Depends on how much math you've had. Arnold is far more mathematically advanced and won't hold the reader's hand.
mathwonk said:as a student i had a routine ode course and never understood anything. arnol'd is more advanced but is so in a conceptually appealing and insightful way. i think it is possible that arnold could actually be more understandable than a routine first course that does not explain any of the ideas but just gives mindless computations.
i.e. the better student you are, the more suitable is arnol'd. and the fact that you are choosing only between arnol'd and hirsch tells me you are likely a strong student.
hirsch is a famous and outstanding mathematician but i think arnol'd's book is much better written pedagogically. if you are so strong that quality of writing is irrelevant to you, and all that matters is the math, there may be some topics covered in hirsch that would make it worth while.
i personally think hirsch is poorly written. but i have his differential topology book because some of the theorems in it are not in my other books.
An ODE (Ordinary Differential Equations) book is a textbook or reference material that focuses on the study of differential equations, which are mathematical equations that describe how quantities change over time.
Hirsch and Arnold are renowned mathematicians who have written books on Ordinary Differential Equations. George Hirsch is a professor emeritus at the University of California, Berkeley, and Stephen Smale is a Fields Medalist and a professor at the City University of Hong Kong. Victor Arnold is a mathematician and professor at the Steklov Mathematical Institute in Russia.
The main difference between the Hirsch and Arnold ODE books is their approach to teaching the subject. While Hirsch's book focuses more on the analytical and numerical methods of solving ODEs, Arnold's book includes a more geometric and qualitative approach.
Both the Hirsch and Arnold ODE books are suitable for beginners, but it ultimately depends on the individual's personal learning style. Hirsch's book may be more suitable for those who prefer a more traditional approach, while Arnold's book may be better for those who prefer a more visual and intuitive approach.
Some familiarity with calculus and basic linear algebra is recommended for studying the Hirsch and Arnold ODE books. However, both books provide a thorough introduction to these topics for those who may need a refresher.