An Advanced Theory of Vibrations
An Advanced Theory of Vibrations
复制标题
先进的振动理论
作者：
K. Weiss
维尔斯特拉斯通过幂级数的函数论方法。第2部分（110页）给出了一个相当完整的椭圆函数，包括模函数和变换理论。第3部分（150页），由于柯朗，补充了赫维茨发展的章节在tho几何精神起源于黎曼。即使在第一版中，第3部分在很大程度上独立于第1部分和第2部分，在第二版（1925年）中，柯朗将第3部分扩展为一个独立的演示文稿。在第三和第四版中，这条尾巴已经长得超过了狗，我将在后面建议，两个比例匀称的生物可以有利地取代以不受控制的方式生长的那条。第3部分现在填补了近300页，是一个帐户，主要是感兴趣的专家，发展的拓扑函数理论。还有其他重要的分支职能理论（例如，积分和亚纯函数），其中一个必须寻找其他地方。R6 hrl明尼苏达州他修订并更新了第三版的文本，并增加了一个150页的附录（两个小册子）。补充阐述了理论在更抽象的设置中的工作，在过去的二十年已经把it. Chapter 1的附录涉及一些问题的共形表示，特别是新的知识primeends（介绍了Caratheodory在1913年）和qm：，siconformal映射。Riemann曲面的1-1共形表示引出了有关Fuchsian群的讨论。附录的第2章包含了一个明确的帐户选择最近的调查紧凑和非紧黎曼曲面。我建议，这本书已经变得笨重和昂贵，在未来的版本中，应该成为两个。第1部分和第2部分将形成一个很好的介绍weierstntps的理论为本科生。实际上，他不太可能需要这么多的细节椭圆函数和根治外科医生可以切除部分第2部分。只有特别优秀的本科生才有时间读第三部分，其他人不应该为了一小部分而买一本大部头的书。任何对第三部分感兴趣的研究人员都会知道第一部分和第二部分的内容，除非作为一种风格的典范，否则不会参考它们。T. C.伯基尔
Weierstrass approach to function-theory through power series. Part 2 (llO pages) gave a fairly full account of elliptic functions, including modular functions and transformation theory. Part 3 (150 pages), duo to Courant, supplemented the Hurwitz development by chapters in tho geometric spirit originated by Riemann. Even in the first edition Part 3 was largely independent of Parts 1 and 2, and in tho second edition (1925) Courant expanded Part 3 into a self-contained presentation. In tho third and fourth editions this tail has outgrown the dog, and I shall suggest later that two well-proportioned creatures could with advantage replace the one which has grown in an uncontrolled way. Part 3 now fills nearly 300 pages and is an account, mainly of interest to the specialist, of the development of topological function-theory. There are other important branches of function-theory (for example, integral and meromorphic functions) for which one must look elsewhere.The preparation of this new fourth edition is due to Prof. H. R6hrl, of Minnesota. He has revised and brought up to date the text of the third edition and has added an appendix of 150 pages (in two cheapters). The additions expound the theory in the more abstract setting in which the work of the past two decades has placed it. Chapter l of the appendix deals with some problems of conformal representation, in particular new knowledge about primeends (introduced by Caratheodory in 1913) and qm:, siconformal mappings. The 1-1 conformal representation of Riemann surfaces leads to a discussion of tho Fuchsian groups involved. Chapter 2 of the appendix contains a clear account of selected recent investigations of compact and non-compact Riemann surfaces. I suggest that the book, which has become unwieldy and costly, should, in future editions, become two. Parts 1 and 2 would form an excellent presentation ofWeierstntPs's theory for the undergraduate. Actually he would be unlikely to need so much of the detail of elliptic functions and a radical surgeon could excise some sections of Part 2. Only exceptional undergraduates would find time to read Part 3, and the others should not have to buy a large book for the sake of a small part of it. Any research worker interested in Part 3 will know what is in Parts 1 and 2 and would not refer to them except perhaps as a model of style., T. C. BuRKILL