Mathematical Analysis II 2nd Edition by Vladimir A Zorich ISBN 3662489910 9783662489918

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Product details:

ISBN 10: 3662489910 

ISBN 13: 9783662489918

Author: Vladimir A. Zorich

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.

 

Table of contents:

Front Matter

Chapter 1 Continuous Mappings (General Theory)

Chapter 2 Differential Calculus from a More General Point of View

Chapter 3 Multiple Integrals

Chapter 4 Surfaces and Differential Forms

Chapter 5 Line and Surface Integrals

Chapter 6 Elements of Vector Analysis and Field Theory

Chapter 7 Integration of Differential Forms on Manifolds

Chapter 8 Uniform Convergence and the Basic Operations of Analysis on Series and Families of Functions

Chapter 9 Integrals Depending on a Parameter

Chapter 10 Fourier Series and the Fourier Transform

Chapter 11 Asymptotic Expansions

Back Matter

Authors and Affiliations

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Tags: Vladimir A Zorich, Mathematical Analysis II