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Mathematical Analysis I
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.
636 pages, Paperback
First published January 1, 1980
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About the author
Vladimir A. Zorich
5 books7 followersVladimir Antonovich Zorich is a Soviet and Russian mathematician, Doctor of Physical and Mathematical Sciences, Professor. Honorary Professor of Moscow State University.
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Displaying 1 - 5 of 5 reviews
February 18, 2015
There's a certain bit of irony when a Russian person reads a Russian book (written by a Moscow State professor) translated to English. Now, I would not claim to enjoy real analysis, but unfortunately some key concepts were required to delve into measure theory (which, in turn, is only a stepping stone).
So what can I say? I liked the explanations in this book, there were no logical discontinuities, and despite the (relative) level of challenge I managed to read this book piece-by-piece without losing the train of thought.
So what can I say? I liked the explanations in this book, there were no logical discontinuities, and despite the (relative) level of challenge I managed to read this book piece-by-piece without losing the train of thought.
July 8, 2015
Easily one of the best analysis books out there; with a nice combination of rigour, motivating physical problems, and clear explanations. Working through the entire book was a demanding yet thoroughly rewarding experience. This book also serves as an excellent reference, which I'm sure I'll be consulting for quite some time.
Looking forward to reading Volume II.
Looking forward to reading Volume II.
June 8, 2022
It is the best mathematical analysis Russian textbook. Zorich one love.
Sadly, it didn't help me with my exam because our program is a little different. Nonetheless, the book made me much more intellectually capable of understanding something more or less mathematically rigorous, so I'm happy that I chose it as the main calculus textbook.
Sadly, it didn't help me with my exam because our program is a little different. Nonetheless, the book made me much more intellectually capable of understanding something more or less mathematically rigorous, so I'm happy that I chose it as the main calculus textbook.
May 22, 2022
This review concerns the second edition of "Mathematical Analysis I" of V. A. Zorich.
This is a very good and modern book that covers in great details all the usual topics (and additional ones as well) of a first course in mathematical analysis.
The author often introduces the topics with an informal discussion of their main concepts and theorems, to which a historical digression on the motivations that lead to the development of that part of mathematical analysis follows.
The mathematical theories are also very often presented in combination with scientific problems in the natural sciences, which helps to frame the theory in its applied framework. For example, Chapter 5 (Differential Calculus) starts with a very detailed and insightful discussion on how the desire to express mathematically the change in trajectory of a moving body leads naturally to the definition of the derivative.
The book addresses its content in great detail and several theorems and examples are presented in each chapter.
The mathematical proofs are generally very clear and elegant and the author leaves few statements without proof and often encourages the reader to work out the proof himself.
The level of rigour in the book is high, even though some concepts are sometimes presented in an informal way, as it is the case with the tangent space in chapter 5.
This is related to the fact that the author tries from the beginning to expose the topics in a very general and modern form, which might lead to the inclusion of concepts from more advanced areas of mathematics which do not belong to a first course of mathematical analysis.
For this reason the book is, in my opinion not suitable as a first book in mathematical analysis, but the reader should have a previous exposure to the presented topics. It remains however an excellent choice for a second book on this subject.
While the author gives several examples, I believe that these are sometimes not sufficient and more counter examples would be beneficial in those sections dealing with more abstract topics, which are plenty, given the author's inclination in presenting the topics from a very general point of view. Exercises are also plenty but no solutions are provided.
Overall I would give this book an 8/10: this is an extremely good second book on mathematical analysis, from which the serious reader can learn a lot and can obtain a more general understanding of the topics presented in other mathematical courses.
More counter examples and some solutions to the exercise would make the book one of the best choice for studying mathematical analysis.
This is a very good and modern book that covers in great details all the usual topics (and additional ones as well) of a first course in mathematical analysis.
The author often introduces the topics with an informal discussion of their main concepts and theorems, to which a historical digression on the motivations that lead to the development of that part of mathematical analysis follows.
The mathematical theories are also very often presented in combination with scientific problems in the natural sciences, which helps to frame the theory in its applied framework. For example, Chapter 5 (Differential Calculus) starts with a very detailed and insightful discussion on how the desire to express mathematically the change in trajectory of a moving body leads naturally to the definition of the derivative.
The book addresses its content in great detail and several theorems and examples are presented in each chapter.
The mathematical proofs are generally very clear and elegant and the author leaves few statements without proof and often encourages the reader to work out the proof himself.
The level of rigour in the book is high, even though some concepts are sometimes presented in an informal way, as it is the case with the tangent space in chapter 5.
This is related to the fact that the author tries from the beginning to expose the topics in a very general and modern form, which might lead to the inclusion of concepts from more advanced areas of mathematics which do not belong to a first course of mathematical analysis.
For this reason the book is, in my opinion not suitable as a first book in mathematical analysis, but the reader should have a previous exposure to the presented topics. It remains however an excellent choice for a second book on this subject.
While the author gives several examples, I believe that these are sometimes not sufficient and more counter examples would be beneficial in those sections dealing with more abstract topics, which are plenty, given the author's inclination in presenting the topics from a very general point of view. Exercises are also plenty but no solutions are provided.
Overall I would give this book an 8/10: this is an extremely good second book on mathematical analysis, from which the serious reader can learn a lot and can obtain a more general understanding of the topics presented in other mathematical courses.
More counter examples and some solutions to the exercise would make the book one of the best choice for studying mathematical analysis.
May 22, 2011
Very well written and very well structured. Thorough, precise, and concise. The problems are especially good.
Displaying 1 - 5 of 5 reviews