Real and Complex Analysis (Chapman & Hall/CRC Pure and Applied Mathematics Book 294) 1st Edition by Christopher Apelian (PDF)

Description

Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide.By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website.This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

User’s Reviews

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

⭐This book does a remarkable job of helping the reader to truly understand the subject matter, in stark contrast to so many mathematical texts which seem to present a collection of pieces without connecting links. The discussions, remarks and examples in each chapter of this book motivate and reinforce the big picture of the chapter in an interesting and well organized way. As a result, each chapter feels fully explored and well-rounded, providing BOTH an intuitive and proof-based understanding of the material. In my opinion, this is not only quite rare but also the best that one could hope for in any mathematics book. I have looked at several sources on real and complex analysis and I feel that the presentation of differentiation in this book is unequivocally the best such presentation that I have read.This text has a plethora of solved examples to explicitly walk the reader through the presented material, and the proofs are crystal clear. Further, the remarks and in-text exercises are actually interesting while also enlightening and fun, as opposed to feeling tedious or unhelpful. In short, if you are looking for a source to make sure that you truly UNDERSTAND both real and complex analysis, then this is a perfect source for you. The top priority of the authors is clearly the understanding of the reader, and this is, again in my opinion, the best that one could hope for in mathematics.As a quick note for those who need a source that deals with general metric spaces: while this text deals almost exclusively with the real (single and multi-dimensional) and complex spaces (with their usual metrics), the text acts as a wonderful companion piece to sources that present more general metric space material. I used this book in tandem with Principles of Mathematical Analysis by Walter Rudin, and I can absolutely say that I would not have understood Rudin’s book anywhere near as well without having used this book as a companion. This is a testament to the strength of the presentation in this book, and I believe that an understanding of any analysis text would be enhanced through the use of this book as a companion.

⭐I found that the book taught me a lot about both real and complex analysis than the traditional approach of treating the two subjects separately. Even if your instructor isn’t using this textbook, it works well as a companion to these two courses as a way to elaborate on certain theorems or to explain certain ambiguities in the text. Definitely try it out!

⭐I use it to teach myself real analysis. It is particularly useful because the book is digestible with a lot of exercises and their solutions.

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