Normal view MARC view ISBD view

Mathematical analysis I / Vladimir A. Zorich.

By: Zorich, Vladimir. A. (Vladimir Antonovich).
Material type: materialTypeLabelBookSeries: Universitext.Copyright date: Berlin; Springer, c2004Description: xviii, 574 pages: illustrations; 25 cm.ISBN: 3540403868; 9783540403869.Subject(s): Mathematical analysis | Análisis matemático | Mathematics | Matemáticas | Physics | Física | Calculus | CálculoDDC classification: 515
Partial contents:
1 Some General Mathematical Concepts and Notation -- 2 The Real Numbers -- 3 Limits -- 4 Continuous Functions -- 5 Differential Calculus -- 6 Integration -- 7 Functions of Several Variables -- 8 Differential Calculus in Several Variables -- Some Problems from the Midterm Examinations -- Examination Topics --
Abstract: 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 . 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. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor. “...Complete logical rigor of discussion...is combined with simplicity and completeness as well as with the development of the habit to work with real problems from natural sciences. ” From a review by A.N. Kolmogorov of the first Russian edition of this course “...We see here not only a mathematical pattern, but also the way it works in the solution of nontrivial questions outside mathematics. ...The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems....In my opinion, this course is the best of the existing modern courses of analysis.” From a review by V.I.Arnold.
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Current location Call number Copy number Status Date due Item holds
Libro académico Libro académico Biblioteca del Campus
515 Z884m 2004 (Browse shelf) Ej. 1 Available
Libro académico Libro académico Biblioteca del Campus
515 Z884m 2004 (Browse shelf) Ej. 2 Available
Libro académico Libro académico Biblioteca del Campus
515 Z884m 2004 (Browse shelf) Ej. 3 Available
Total holds: 0

Includes bibliographical references and indexes.

1 Some General Mathematical Concepts and Notation -- 2 The Real Numbers -- 3 Limits -- 4 Continuous Functions -- 5 Differential Calculus -- 6 Integration -- 7 Functions of Several Variables -- 8 Differential Calculus in Several Variables -- Some Problems from the Midterm Examinations -- Examination Topics --

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 . 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. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor. “...Complete logical rigor of discussion...is combined with simplicity and completeness as well as with the development of the habit to work with real problems from natural sciences. ” From a review by A.N. Kolmogorov of the first Russian edition of this course “...We see here not only a mathematical pattern, but also the way it works in the solution of nontrivial questions outside mathematics. ...The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems....In my opinion, this course is the best of the existing modern courses of analysis.” From a review by V.I.Arnold.

There are no comments for this item.

Log in to your account to post a comment.