Title: a poor job!
Product review: Unfortunately this book is used at many good schools, but it should not be! Given that there are many excellent texts it is hard to understand why this book is chosen so often. The author is very brief with his proofs as though the reader is reviewing the material and not learning it for the first time. On the other hand, he explains some simple topics excessively when it's not at all necessary. I think the reason for the style of this book is that Marsden is really an applied mathematican. I would not use this book for self-study, unless I had to. There are also many errors in the book. It is possible to make use of the book by supplementing it with other books (almost any book on analysis would do!). In short, Marsden does a beautiful job of turning analysis into an ugly subject! Be warned!!
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