A Friendly Introduction to Analysis 2nd Edition by Witold Kosmala (PDF)

Description

For two-semester/three-quarter, first undergraduate courses in Advanced Calculus or Real Analysis.This book is an easy, readable, intimidation-free analysis textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This text covers both single and multivariable analysis in a student friendly setting.

User’s Reviews

Editorial Reviews: From the Back Cover /*4579F-0, 0-13-045796-5, Kosmala, Witold J., Advanced Calculus: A Friendly Approach, 2/E*/ This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting. Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration. For individuals seeking math fun at a higher level.

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

⭐The idea of this book is great – you are sitting in front of Rudin, you have no idea what to do and all of a sudden you open this book and things become clear! Umm, not quite. First, this book has had problems with a multitude of typos (see the author’s web site). Second, the title is stupid. There is no such thing as a ‘friendly introduction to analysis’. That’s an oxymoron if ever there was one. This book is very good at explaining basic ideas and giving you some insights BUT IT STILL AIN’T RUDIN (and its discussion/proofs of convergence tests is weak since they all link back to geometric sums and that is not mentioned here). If you want to study analysis you eventually have to make large pot of coffee, put butt in chair, take out pencil and a raft of paper and start working – without tv, ipod, music, dog, wife, etc. Will this book help some? Sure, it is a nice reference. Will it teach you enough to say you know analysis. No.

⭐This book is required for a 2 semester course that began fall 2010. I bought it from Amazon.com.The first problem is the content layout. The author has you jumping forward and backward through the chapters while explaining the current chapter. This is not an occasional thing. It’s extremely frustrating and totally unnecessary. The author does a decent job of explaining things and if the book was organized better, it might be a decent textbook.The second problem is that this book, published by Pearson Prentice Hall began falling apart within a couple weeks of my purchase. By the end of the semester, it was in two parts and now individual pages in each part are begining to come apart. I don’t know when Prentice Hall became “Pearson Prentice Hall” but I have text from Prentice Hall that have held up well for a couple decades and have been used during this time. At some point, they started putting out very poor quality books and this is one.If you have a choice, I’d suggest finding another text. If you are a instructor, please don’t choose this text and force students to waste their money. While the book is cheaper than many others, if it falls apart, it is still a bad deal overall.

⭐the last forty pages weren’t even connected to the book. and it came in a really beat up condition.

⭐It’s nothing fantastic. I wish that there would be some better answers provided to problems. I end up having to look online for random proof sites to check my answers.

⭐Not very easy to follow. The book has you jumping around from place to place and made learning how to write proofs a nightmare!! If this book is what is recommended for your course you will be watching a lot of you tube videos for explanations as well as googling other books.

⭐Great book! Exactly what I needed in class! A little more beat up then I was hoping for.

⭐”Friendly”

⭐I have taught Analysis for over 30 years and used a number of books. I am returning to this one next year after trying another one this year for variety. Kosmala is far from perfect, but I am unaware of a book that is significantly better.Analysis is hard. That means students will complain that somehow the author of an analysis books has failed to make it easy. One complaint above was “Particularly annoying is his comparing exercises to many previous (and future!!) problems in the text.” That is not a fault, rather a virtue. Analysis is proof and proof relates current theorems to previous material. I would be very disappointed if a text did not refer to previous material! And, showing you where it is going is not bad, either.Another complaint I read about analysis texts is the homework is hard and not modeled in the exposition. This is usually false. The homework is usually a proof of some related result which is just like a theorem, but minor, or outside the main thread of the exposition. Surely the proofs of the major results *do* model how to do the minor ones. Reviews from students who find Analysis texts hard seem to miss the point: the theorems model the results. Learn the proofs of the theorems. This is not an algorithmic course where they show you what to do and you do it. (Computers can do algorithms already. Hopefully, Analysis is more than that!)Kosmala is good for having all the usual first semester Analysis material well-organized and having enough, including some multivariate calculus, to compete a second semester (not at a top-ranked school, but at a mid-ranked school). A lot of Analysis texts contain one-semester of material plus a bit more– but many of the courses are two semesters, so those books are unsuitable. I am using Kirkwood now (Spring 2014) and it just doesn’t have two semesters of material. (I have other serious objections to Kirkwood, too)As others have noted, the paperback version pages fall out. My copies have made it a whole year, but not the second year. The hardcover stays together. There are many typos, The author can send along a file with corrections to earlier printings, but it is irritating to have to make so many minor typographical fixes. If you could tell what printing you are buying, get the 5th or higher if you can.I never did find a great Analysis text that serves for two semesters. There are some very good ones that are too sophisticated (hard) for my students. There are some that are too short for a two-semester class. Are there things in Kosmala that I would do differently? Sure, but there are even more such things in the other texts. The homework is good and covers all levels from easy to medium to a significantly difficult addition to the material. Although I have used a number of other texts, with this one I didn’t feel the need to pull additional homework from other sources.Kosmala has more explanation than most. If you wanted to learn by reading, Kosmala is probably good for that. If you want a concise exposition, Kosmala is not particularly concise.From all the Amazon reviews of all the Analysis texts I read, I infer that students find Analysis hard and will find some reason to complain about each of them.Two-thirds of the complaints are, in my opinion, not valid. The other third are valid, but I don’t know of a text that doesn’t have valid complaints about it. For me, the two semesters of material is important. I’m returning to Kosmala.

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