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.
發表於2024-10-02
Ordinary Differential Equations 2024 pdf epub mobi 電子書 下載
以下是一些作為學渣的體會,對於大神來說完全不適用: 1. 首先吐槽一下語言:感覺這本書的英文翻譯不是很好懂==像Rudin,Stein等人的書,看著還比較痛快,但是這本用詞似乎過於生動瞭一點,句子結構有些地方比較復雜,讀起來有點磕磕絆絆的感覺。 2. 對於應付考試而言,本書沒...
評分個人覺得很難入門。我看的是英文版的,第三版吧,記不大清楚瞭。 作者其實講述還是挺清楚的。但是我個人覺得對它的思路不太適應,所以看起來還覺得有些睏難,沒有連續的看,但是中途看瞭好多次。至今沒有看完……還早 在看這本之前,我是學習過常微分方程。也許一點沒有學過...
評分以下是一些作為學渣的體會,對於大神來說完全不適用: 1. 首先吐槽一下語言:感覺這本書的英文翻譯不是很好懂==像Rudin,Stein等人的書,看著還比較痛快,但是這本用詞似乎過於生動瞭一點,句子結構有些地方比較復雜,讀起來有點磕磕絆絆的感覺。 2. 對於應付考試而言,本書沒...
評分個人覺得很難入門。我看的是英文版的,第三版吧,記不大清楚瞭。 作者其實講述還是挺清楚的。但是我個人覺得對它的思路不太適應,所以看起來還覺得有些睏難,沒有連續的看,但是中途看瞭好多次。至今沒有看完……還早 在看這本之前,我是學習過常微分方程。也許一點沒有學過...
評分隻想學解方程的彆看,想詳細瞭解定性穩定性理論的也彆看,如果是想直觀瞭解一點微分流形,倒是可以考慮翻翻~
圖書標籤: 數學 數學 幾何 ODE
Ordinary Differential Equations 2024 pdf epub mobi 電子書 下載