圖書標籤: 數學 復分析 complex_analysis Analysis 數學經典教材 Mathematics Elias.M.Stein 分析
发表于2024-12-23
Complex Analysis pdf epub mobi txt 電子書 下載 2024
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, "Complex Analysis" will be welcomed by students of mathematics, physics, engineering and other sciences. "The Princeton Lectures in Analysis" represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which "Complex Analysis" is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
試著用我個人視角的大框去感受這些數學規律背後的意義和適用範圍。
評分在老師引導下嘗試接觸,收益頗豐。
評分GREAT~除瞭觀點比較高講的內容比較多 -- 感覺讀起來挺纍的。。。
評分經典啊
評分經典啊
书中P47到P48证明柯西型求导公式貌似用到了一个假设:取极限与积分可以交换顺序。h趋于零是在积分号外面的,但证明到后来,貌似就变成了在里面的意思了。请问这是前面有定理支持还是怎么回事?小弟没细读前面。
評分书中P47到P48证明柯西型求导公式貌似用到了一个假设:取极限与积分可以交换顺序。h趋于零是在积分号外面的,但证明到后来,貌似就变成了在里面的意思了。请问这是前面有定理支持还是怎么回事?小弟没细读前面。
評分读书时学的不扎实。 现在做研究了,对于关联复分析的东西老是发憷, 花了大概3天时间,恶补了一下复分析的知识。 简单说一下 1. 首先是这本书:5星好评。 读其他的书的时候(尤其是国内的复分析教材), 基本是定理+习题;定理+习题之类的。 这本书的好处在于,对于每一个章节...
評分书中P47到P48证明柯西型求导公式貌似用到了一个假设:取极限与积分可以交换顺序。h趋于零是在积分号外面的,但证明到后来,貌似就变成了在里面的意思了。请问这是前面有定理支持还是怎么回事?小弟没细读前面。
評分读书时学的不扎实。 现在做研究了,对于关联复分析的东西老是发憷, 花了大概3天时间,恶补了一下复分析的知识。 简单说一下 1. 首先是这本书:5星好评。 读其他的书的时候(尤其是国内的复分析教材), 基本是定理+习题;定理+习题之类的。 这本书的好处在于,对于每一个章节...
Complex Analysis pdf epub mobi txt 電子書 下載 2024