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This second 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 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.
List of 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.- Appendices.- References.- Subject Index.- Name Index.
About the author
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”.
Summary
This second 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 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.
Additional text
“This is a thorough and easy-to-follow text for a beginning course in real analysis … . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. … Will be popular with students because of the detailed explanations and the worked examples.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)
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"This is a thorough and easy-to-follow text for a beginning course in real analysis ... . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. ... Will be popular with students because of the detailed explanations and the worked examples." (Allen Stenger, MAA Reviews, maa.org, May, 2016)
