Mathematical Analysis II 2nd Edition by Vladimir 3662489937 9783662489932

Mathematical Analysis II 2nd Edition by Vladimir A. Zorich – Ebook Instant Download/Delivery ISBN(s): 3662489937, 9783662489932

Product details:

• ISBN 10:  3662489937
• ISBN 13:  9783662489932
• Author: Vladimir

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:

9. *Continuous Mappings (General Theory)

10. *Differential Calculus from a More General Point of View

11. Multiple Integrals

12. Surfaces and Differential Forms in R n $\mathbb{R}^{n}$

13. Line and Surface Integrals

14. Elements of Vector Analysis and Field Theory

15. *Integration of Differential Forms on Manifolds

16. Uniform Convergence and the Basic Operations of Analysis on Series and Families of Functions

17. Integrals Depending on a Parameter

18. Fourier Series and the Fourier Transform

19. Asymptotic Expansions

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