Mathematical Analysis II (Paperback)

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.

The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics.

This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

這本非常受歡迎的兩卷本的第二版英文版，提供了一個徹底的分析初級課程，從實數到高級主題，如流形上的微分形式、漸進方法、傅立葉、拉普拉斯和勒讓德轉換、橢圓函數和分布。這門課程特別值得注意的是對自然科學的明確表達取向，以及對微積分基本概念和定理的本質和根源的非正式探索。清晰的陳述與豐富的教學練習、問題和鮮有觸及的應用領域相匹配，這些領域在實分析教科書中很少提及。

第二版和第一版英文版的主要區別在於每卷增加了一系列附錄。第一卷有六個附錄，第二卷有五個附錄。這些附錄的主題多樣。它們旨在對數學和物理學的學生以及教師都有用，因為他們可能有不同的目標。其中一些附錄是前瞻性和回顧性的調查。最後一個調查建立了分析與數學其他部分之間的重要概念聯繫。

這本第二卷以統一的數學形式呈現了經典分析，展示了分析如何與代數、微分幾何、微分方程、複分析和泛函分析等現代數學領域互動。這本書為在這些方向中進行高級研究提供了堅實的基礎。

VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences.

VLADIMIR A. ZORICH是莫斯科國立大學的數學教授。他的專業領域包括分析學、共形幾何學、拟共形映射以及熱力學的數學方面。他解決了空間拟共形映射的全局同胚問題。他在機械工程技術方面擁有一項專利，並以他的著作《自然科學中的數學分析問題》而聞名。