Applied Analysis by John K Hunter (PDF)

Description

“The presentation is clear and proofs for most of the results used are given … The book is accessible to students from a wide variety of backgrounds and has as prerequisites only basic calculus, linear algebra and ordinary differential equations.” Mathematical Reviews This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.

User’s Reviews

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

⭐Decent book. The explanations are not very clear and not very detailed.The strength of the book is that it surveys a lot of topics in Applied Analysis, the downside is that it’s not very clearly written and sometimes the proofs are harder to follow than other graduate books covering the same topic at the same level.This book is good, but you’ll find yourself referencing other books from time to timeWe used this in my graduate applied analysis course.

⭐Odd book with very odd examples that may confuse instead of instill understanding. I’ve attempted read similar books on the subject such as Lieb/Loss and Friedman and while no book is perfect in and of itself perhaps using all three at the same time would be better than using any one in particular. As I’ve said earlier the examples are very weird and without previous exposure to the concepts beforehand will most likely confuse the reader. I appreciate “applied” books, but I think this one misses at times.

⭐This is a good book to learn applied topics from Functional Analysis.Although the title says “applied”, it is still analysis with theorems & proofs, NOT computational techniques.Instead, it covers many areas of application in functional analysis.The proofs are much easier than other formal books, because it assumes that the readers are outside Math dept.I would call the book “analysis on applied topics”

⭐I used this book as the primary text for my graduate analysis sequence. The examples and exercises were very instructive. Occasionally, I found myself looking to other standard texts in analysis or functional analysis for more details, but that is true of every textbook. It’s available free on Hunter’s website, but it’s so cheap that it’s a bit silly to take the electronic route.

⭐Excellent text. Readable with out much fluff but doesn’t sacrifice rigor where needed.

⭐This is an excellent book that whips you through a lot of Analysis very quickly, but at the same time is plenty detailed. It is also excently written.

⭐Exactly as advertised. Outstanding service.

⭐This would be a perfect book to learn the functional analysis one would want for doing differential equations. The authors have good taste about what material to include and the writing is good. The final chapter is extraordinarily valuable because it is unusual for textbooks on functional analysis to deal with differential calculus and the calculus of variations. This chapter covers the Fréchet derivative, the integration of functions taking values in a Banach space, the inverse and implicit function theorems in Banach spaces, and Newton’s method. Aside from this chapter being well written like the rest of the book, there are in fact few places to learn this material from. Another book that covers this material is “Computational Functional Analysis” by Moore and Cloud.I have read in detail sections from different parts of the book and it seems like the chapters of the book can be read fairly independently. Notation and ideas from earlier parts of the book don’t seem tacitly to be used later, and thus one should be able to read just those parts of the book one cares about, rather than having to read everything up to that point.

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