Mathematical Analysis, Second Edition 2nd Edition by Tom Apostol (PDF)

Description

It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’m writing this review from the perspective of a undergraduate student who has never been exposed to analysis and not as a seasoned mathematician looking back.From what I understand the treatment of calculus at the undergraduate level has changed significantly in the last few decades with the emphasis being more towards an intuitive understanding of the underlying theory and a heavy emphasis in crunching out calculation quickly and accurately (the ideal treatment of calculus for engineers and applied scientist). The concepts of limits and sets in particular is given only the lightest of treatments. This approach leaves a pretty huge abstract leap for anyone approaching analysis for the first time. Apostol’s book provides the perfect bridge from that type of calculus to the fundamental concepts of analysis.For this reason Mathematical Analysis is one of my favorite books, period! I came across this book while struggling to get through my first course in introductory analysis and I have to say it saved my life! Some people criticizes the author for “spoon feeding” the concepts to the reader, but when you have never had any exposure to analysis before a little spoon feeding goes a long way. Even now as I’m working my way through upper division and first year graduate courses in statistics, this book is still my favorite reference!Apostol’s treatment of basic topology as an extension of set theory is particularly good! Once you have a clear understanding of limits as they relate to topology then you’ll finally “get” the whole delta-epsilon arguments from calculus.As an introductory text to the world of mathematical analysis I don’t think this book can be beat. Rosenlicht is a little too terse and Rubin is a little too abstract for a beginner. Dont’ get me wrong. Rubin is amazing, but if you do not have a solid familiarity with the basic concepts of sets and their relationship to limits, Rubin’s book is going to be out of reach for the beginner. First tackle Apostol then move on to Rubin!

⭐This textbook is a mixed bag. It is good and clear if you already understand the concepts. It is good for reference if you know a lot of the stuff already BUT if you just starting out on the stuff it’s pretty bad. I gives a lot of examples (which professors like) but BARELY and I mean BARELY shows work or shows examples and how to solve things. I believe a good textbook should teach someone HOW to solve things step by step (or in simpler terms, teach).That being said it is a great reference book, not a good book if you are learning the material for the first time.

⭐As stated by prior reveiwers, this books does assume that the reader is Mathematically mature (a saying most young Mathematicians despise), in the sense that he/she must be able to follow the logical development of any given arguement, be able to ‘see’ where and how topics are related as well as fill in any blanks that may present themsevles in a given definition/proof. Apostol, as compared to Rudin, does a nice job of filling in these blanks by adequately providing all of the necessary details within a proof. This book will provide the willing student with a solid foundation in elementary analysis as well as the confidence to persue higher analysis. The only draw back to Apostols book, aside from cost, is that the constant Theorem – Proof – Theorem format can be overwhelming at times and cause some readers to cover material too quickly. Despite the book’s cost I would highly recommend this book over “baby” Rudin (that is, Principles of Mathematical Analysis) since Rudin is notorious for not filling in the blanks within a given proof and instead provides seemingly ‘slick proofs’.

⭐It is​ good books if you feel that Rudin is so difficult to read. Also, I think reading the multivariable part of this book is helpful for reading Spivak’s Calculus.

⭐I found it more accessible than baby Rudin. Clear and in depth explanations for fundamental concepts of Pure Maths. Provides a solid foundation for study of more advanced topics.

⭐This book goes deeper in the Analysis world. It is a reference book for studying Real Analysis, just the way the calculus book is. The language, explanations and examples fulfill your expectations when you want to study at a higher level way.

⭐Very helpful

⭐This book it’s just awesome. It explains everything you need from the beginning with a lot of examples for clarification.

⭐The book is undoubtedly a classic! Nevertheless, it arrived with a damaged cover… That is why I am giving three stars… especially because it is a quite expensive book

⭐Texto riquíssimo e que vale muito a pena. Apesar de não ser completo, constitui referência mundial na teoria elementar da Análise Real.Livro conforme descrito no anúncio.A classic book. An evergreen. Very clear and rigorous. Ideal for self study, and as a reference book. Suggested to anyone interested in this field.

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