Conformal Mapping on Riemann Surfaces (Dover Books on Mathematics) by Harvey Cohn (PDF)

Description

The subject matter loosely called “Riemann surface theory” has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn’s lucid and insightful book presents an ideal coverage of the subject in five parts. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in Part II and is examined in terms of intuitive physical and topological technique in Part III. In Part IV the author shows how to define real functions on manifolds analogously with the algebraic and analytic points of view outlined here. The exposition returns in Part V to the use of a single complex variable z. As the text is richly endowed with problem material — 344 exercises — the book is perfect for self-study as well as classroom use.Harvey Cohn is well-known in the mathematics profession for his pedagogically superior texts, and the present book will be of great interest not only to pure and applied mathematicians, but also engineers and physicists. Dr. Cohn is currently Distinguished Professor of Mathematics at the City University of New York Graduate Center.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐My major fault with this book is with the hydrodynamics/ aerodynamicscoverage, since he leaves out Joukowski air foil theory completely.On the plus side his coverage of Möbius geometry, the anharmonic invariant and the cross ratiois outstanding. Also the coverage of the Euler-Poincare characteristic equationwas enlightening with the addition of “edges” or cross cap borders.The Poisson kernel section is very good as well.I think the major virtue of the book is the amount of important material coveredfor the Dover books price…

⭐A good treatment of many of the classic aspects of Riemann surfaces, From The Riemann sphere to the torus and elliptic functions to Riemann-Roch. The later chapters are quite advanced.

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