要是谁当年也被标准的常微分方程（ODE）导论课折磨过、学完还一头雾水，我强烈推荐 Vladimir Arnold 讲这门课的那本书 [1]。它对底层几何原理给出了很多深刻见解，只要是适应……的人都能读得大有收获。
For anyone who was subjected to the standard intro ordinary differential equations (ODEs) course and left unenlightened, I’d highly recommend Vladimir Arnold’s book on the subject [1]. It gives a lot of insight into the underlying geometry and can be read profitably by anyone comfortable…
……如果你在找进阶的微分方程书籍，我推荐 Lawrence C. Evans 的《Partial Differential Equations》，对偏微分方程（PDE）的覆盖非常全面。如果想更专注常微分方程，Vladimir I. Arnold 的《Ordinary Differential Equations》是个绝妙的选择。而如果想深入钻研随机微分方程，不妨看看 Bernt Øksendal 的《Stochastic Differential Equations》。
…if you're looking for advanced books on differential equations, I'd recommend "Partial Differential Equations" by Lawrence C. Evans for a comprehensive coverage of PDEs. For a more specialized focus on Ordinary Differential Equations, "Ordinary Differential Equations" by Vladimir I. Arnold is a fantastic choice. And for a deep dive into Stochastic Differential Equations, check out "Stochastic Differential Equations" by Bernt Øksendal.
……定理非常精彩。它还包含了一个关于素数渐近密度的切比雪夫定理的极佳证明，甚至还有整数分拆的罗杰斯-拉马努金恒等式。4. Vladimir Arnold 的《Ordinary Differential Equations》：本科的 ODE 课往往教得像照谱做菜，这样的话根本带不来什么启发。而这本书从几何层面解释了到底是怎么回事。在读它之前我根本体会不到 ODE 的美……
…Theorem are lovely. It also includes a very nice proof of Chebyshev's theorem on the asymptotic density of primes and even the Rogers-Ramanujan identities for integer partitions. 4. Vladimir Arnold, Ordinary Differential Equations: Undergrad ODE classes are often taught in a cookbook fashion and if so, don't offer much enlightenment. This book explains what's going on at geometrical level. I didn't appreciate ODEs until I read…
I can only find the first edition on Amazon, but there's apparently a third edition? http://www.matem.unam.mx/ernesto/EDO/Ar-EDO.pdf https://www.amazon.com/Ordinary-Differential-Equations-MIT-P...
- 《普林斯顿数学指南》（Princeton Companion to Mathematics）
- 《解题的艺术与技巧》（The Art and Craft of Problem Solving）
- 《散度、旋度和所有那些》（Div, Grad, Curl and all that）
- 《复分析可视化》（Visual Complex Analysis）
- 《常微分方程》（Ordinary Differential Equations）
- 《数学及其历史》（Mathematics and Its History）
- 《几何与想象》（Geometry and the Imagination）
- 《电动力学导论》（Introduction to Electrodynamics）
- 彭罗斯的《通向实在之路》（Road to Reality）
- Princeton Companion to Mathematics - The Art and Craft of Problem Solving - Div, Grad, Curl and all that - Visual Complex Analysis - Ordinary Differential Equations - Mathematics and Its History - Geometry and the Imagination - Introduction to Electrodynamics - Penrose's Road to Reality
顺着这个思路，我能不能再推荐一下 V.I. Arnol'd 的《常微分方程》（Ordinary Differential Equations）。
In that vein, may I also suggest Ordinary Differential Equations by V.I. Arnol'd.
要是谁当年也被标准的常微分方程（ODE）导论课折磨过、学完还一头雾水，我强烈推荐 Vladimir Arnold 讲这门课的那本书 [1]。它对底层几何原理给出了很多深刻见解，只要是适应……的人都能读得大有收获。
For anyone who was subjected to the standard intro ordinary differential equations (ODEs) course and left unenlightened, I’d highly recommend Vladimir Arnold’s book on the subject [1]. It gives a lot of insight into the underlying geometry and can be read profitably by anyone comfortable…
……如果你在找进阶的微分方程书籍，我推荐 Lawrence C. Evans 的《Partial Differential Equations》，对偏微分方程（PDE）的覆盖非常全面。如果想更专注常微分方程，Vladimir I. Arnold 的《Ordinary Differential Equations》是个绝妙的选择。而如果想深入钻研随机微分方程，不妨看看 Bernt Øksendal 的《Stochastic Differential Equations》。
…if you're looking for advanced books on differential equations, I'd recommend "Partial Differential Equations" by Lawrence C. Evans for a comprehensive coverage of PDEs. For a more specialized focus on Ordinary Differential Equations, "Ordinary Differential Equations" by Vladimir I. Arnold is a fantastic choice. And for a deep dive into Stochastic Differential Equations, check out "Stochastic Differential Equations" by Bernt Øksendal.
……定理非常精彩。它还包含了一个关于素数渐近密度的切比雪夫定理的极佳证明，甚至还有整数分拆的罗杰斯-拉马努金恒等式。4. Vladimir Arnold 的《Ordinary Differential Equations》：本科的 ODE 课往往教得像照谱做菜，这样的话根本带不来什么启发。而这本书从几何层面解释了到底是怎么回事。在读它之前我根本体会不到 ODE 的美……
…Theorem are lovely. It also includes a very nice proof of Chebyshev's theorem on the asymptotic density of primes and even the Rogers-Ramanujan identities for integer partitions. 4. Vladimir Arnold, Ordinary Differential Equations: Undergrad ODE classes are often taught in a cookbook fashion and if so, don't offer much enlightenment. This book explains what's going on at geometrical level. I didn't appreciate ODEs until I read…
我在亚马逊上只能找到第一版，不过貌似已经出第三版了？http://www.matem.unam.mx/ernesto/EDO/Ar-EDO.pdf https://www.amazon.com/Ordinary-Differential-Equations-MIT-P...
I can only find the first edition on Amazon, but there's apparently a third edition? http://www.matem.unam.mx/ernesto/EDO/Ar-EDO.pdf https://www.amazon.com/Ordinary-Differential-Equations-MIT-P...
- 《普林斯顿数学指南》（Princeton Companion to Mathematics） - 《解题的艺术与技巧》（The Art and Craft of Problem Solving） - 《散度、旋度和所有那些》（Div, Grad, Curl and all that） - 《复分析可视化》（Visual Complex Analysis） - 《常微分方程》（Ordinary Differential Equations） - 《数学及其历史》（Mathematics and Its History） - 《几何与想象》（Geometry and the Imagination） - 《电动力学导论》（Introduction to Electrodynamics） - 彭罗斯的《通向实在之路》（Road to Reality）
- Princeton Companion to Mathematics - The Art and Craft of Problem Solving - Div, Grad, Curl and all that - Visual Complex Analysis - Ordinary Differential Equations - Mathematics and Its History - Geometry and the Imagination - Introduction to Electrodynamics - Penrose's Road to Reality