Friendly Approach To Complex Analysis, A by Amol Sasane (PDF)

Description

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text.

User’s Reviews

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

⭐I own a numbers of books on undergraduate complex analysis and there is no definitive book for me, unlike some other areas which have 2 or 3 classic texts. This particular book is very nice in that it gives you an intuitive feel for the subject, although it assumes some fairly advanced math has already been covered which i think is a shame. For example chapter 1 assumes knowledge of abstract algebra. My main issue with the book is that some of the definitions (!!) and problem sets are riddled with typos. If the typos were cleaned up, I would give this text 4 stars. If you’re willing to overlook these issues and are toward the tail end of a mathematical degree, then this is a good book. Avoid it if you’ve only covered the standard calculus sequence, you won’t be ready for this book yet, despite the title. This may be an intro book for complex analysis, but it NOT an intro book for a mathematics education.

⭐The ‘friendly introduction’ to Complex Analysis advertised on the cover lasts about 5 pages. Then it quickly becomes the ‘unfriendly nightmare’.Pros of this book is that the homework problems are somewhat do-able, given enough time with the relevant section, and that some concepts are explained in a fairly clear tone due to the conversational nature taken at varying points in the text. That’s about it for the good.On the other hand, the book likes to “leave proofs to the reader” of important concepts which is infuriating given that as someone learning new material it is not my job to “prove” the very things I’m trying to understand. That is the author’s job. Has anyone told Amol Sasane? There are crucial details left out when “complete” proofs are presented, making them very difficult to understand. The formatting of the book is also very poor, with homework problems literally presented in the margins on random pages of the text instead of a nice, neat section at the end of each chapter.I would avoid this book and purchase something better.

⭐I’m not yet finished, though this is extremely well done. Thus far the book is very clear and very straightforward. Some prior exposure to real analysis (say a chapter on sequences) and rudiments of topology in the plane may be needed to really appreciate the book. It is a ‘friendly’ book though and I like it.

⭐A friendly introduction it is. I come from a CS background without EVER having taking complex analysis or partial differential equations. The intuition and context the author gives when explaining the material is amazing. I am almost jaleous at his LaTeX skills, which are used to visualise literally every concept in the book. The book is advanced enough (I had some difficulties understanding later chapters) that I think even advanced students can pick something up here. Moreover, this is one of the only times I ever considered exercises to be really original (and fun!!!). A MUST READ for anyone seriously considering mathematics!

⭐It feels that the authors have passion for it and the result is a clearly written and well structured book. Exercises and problems constitite an important part of the book and as an extra bonus for students more than third of the book consists of worked out solutions.Raul Hindov

⭐”Clear,concise and enjoyable.It is the best first introduction to complex analysis.It has detailed solutions making it easy to check work and self study.The conversational style used by the authors makes the reading pleasant.There are lots of pictures making it easy to visualise and understand the subject.”

⭐This is one of the best textbook I’ve had in college; it is something one want to keep in the bookshelf for later reference. I’ve learned a great deal of complex analysis from the book. Prof. Sasane presents the material in a approachable way, with exercises that help me understand the material more deeply.

⭐I like very much the freindly stile !!Bo A

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