There are dozens of books on ODEs, but none with the elegant geometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on theroutine presentation of algorithms for solving special classes of equations.Of course, the reader learns how to solve equations, but with much more understanding of the systems, the solutions and the techniques. Vector fields and one-parameter groups of transformations come right from the startand Arnol'd uses this "language" throughout the book. This fundamental difference from the standard presentation allows him to explain some of the real mathematics of ODEs in a very understandable way and without hidingthe substance. The text is also rich with examples and connections with mechanics. Where possible, Arnol'd proceeds by physical reasoning, using it as a convenient shorthand for much longer formal mathematical reasoning. This technique helps the student get a feel for the subject. Following Arnol'd's guiding geometric and qualitative principles, there are 272 figures in the book, but not a single complicated formula. Also, the text is peppered with historicalremarks, which put the material in context, showing how the ideas have developped since Newton and Leibniz. This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems.
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2014年说明： 此文写于很多年前，当时我性格不好，语言不够平和。承蒙各位网友不嫌弃，点了不少所谓的“有用”。今天的我更希望能用友善委婉的语气表达同样的意思，但也无心去修改原文了。希望今后各位读者不要受到误导。 --------------------------------------------------...
评分只想学解方程的别看，想详细了解定性稳定性理论的也别看，如果是想直观了解一点微分流形，倒是可以考虑翻翻~
评分以下是一些作为学渣的体会，对于大神来说完全不适用： 1. 首先吐槽一下语言：感觉这本书的英文翻译不是很好懂==像Rudin，Stein等人的书，看着还比较痛快，但是这本用词似乎过于生动了一点，句子结构有些地方比较复杂，读起来有点磕磕绊绊的感觉。 2. 对于应付考试而言，本书没...
评分以下是一些作为学渣的体会，对于大神来说完全不适用： 1. 首先吐槽一下语言：感觉这本书的英文翻译不是很好懂==像Rudin，Stein等人的书，看着还比较痛快，但是这本用词似乎过于生动了一点，句子结构有些地方比较复杂，读起来有点磕磕绊绊的感觉。 2. 对于应付考试而言，本书没...
评分2014年说明： 此文写于很多年前，当时我性格不好，语言不够平和。承蒙各位网友不嫌弃，点了不少所谓的“有用”。今天的我更希望能用友善委婉的语气表达同样的意思，但也无心去修改原文了。希望今后各位读者不要受到误导。 --------------------------------------------------...
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