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OverviewThis 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. Full Product DetailsAuthor: V. A. Zorich , Roger Cooke , Octavio PaniaguaPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 2nd ed. 2016 Weight: 1.116kg ISBN: 9783662569665ISBN 10: 3662569663 Pages: 720 Publication Date: 13 March 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of Contents9 Continuous Mappings (General Theory).- 10 Differential Calculus from a General Viewpoint.- 11 Multiple Integrals.- 12 Surfaces and Differential Forms in Rn.- 13 Line and Surface Integrals.- 14 Elements of Vector Analysis and Field Theory.- 15 Integration of Differential Forms on Manifolds.- 16 Uniform Convergence and Basic Operations of Analysis.- 17 Integrals Depending on a Parameter.- 18 Fourier Series and the Fourier Transform.- 19 Asymptotic Expansions.- Topics and Questions for Midterm Examinations.- Examination Topics.- Examination Problems (Series and Integrals Depending on a Parameter).- Intermediate Problems (Integral Calculus of Several Variables).- Appendices: A Series as a Tool (Introductory Lecture).- B Change of Variables in Multiple Integrals.- C Multidimensional Geometry and Functions of a Very Large Number of Variables.- D Operators of Field Theory in Curvilinear Coordinates.- E Modern Formula of Newton–Leibniz.- References.- Index of Basic Notation.- Subject Index.- Name Index.ReviewsAuthor InformationVLADIMIR 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. Tab Content 6Author Website:Countries AvailableAll regions |
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