图书标签: PDE  数学  nonlinear  色散方程  偏微分方程7  monograph  math  Math   

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陶哲轩神作

要读通的话难度很大。很多习题是著名文章的结果，只是让读者去查找文献。内容讲得真的很好，临界色散方程的基本方法一应俱全。但不应“仅仅通过”这本书来学习色散方程的基础知识，主要还是去读原始文章。 可惜接下来若干年都与色散方程无缘了，不过它的附录我仍然经常查阅。无论如何，我永远也不会忘记这本书当初给我带来的震撼。

因为想了解nonlinear wave选了这本书，但不是个明智的选择，尤其在没学过调和分析的情况下。但Tao很有洞见，尤其第一章所表述的内容和之后章节的联系。细节太少，typo多到后来不想去看勘误表，过多的例子和证明放在了练习。初学者可以参考Tadahiro Oh "Nonlinear Schrödinger Equations"这门课的笔记和references。 E. L. 认为最后一章关于wave maps的内容过于陈旧。

PDE的代数（对称，守恒律，显示表达）和分析（渐进，存在和唯一）；方程的几何物理直觉和严格分析之间平衡。自治方程=时间平移不变量=嵌入；第一章一阶拟线性方程组的柯西问题关键概念是解析性；诺特定理本质联系了对称和守恒；

要读通的话难度很大。很多习题是著名文章的结果，只是让读者去查找文献。内容讲得真的很好，临界色散方程的基本方法一应俱全。但不应“仅仅通过”这本书来学习色散方程的基础知识，主要还是去读原始文章。 可惜接下来若干年都与色散方程无缘了，不过它的附录我仍然经常查阅。无论如何，我永远也不会忘记这本书当初给我带来的震撼。

" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...

" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...

" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...

" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...

" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...