Multidimensional Real Analysis I: Differentiation (Cambridge Studies in Advanced Mathematics, Series Number 86) 1st Edition by J. J. Duistermaat (PDF)

Description

Volume 1 provides a comprehensive review of differential analysis in multidimensional Euclidean space.

User’s Reviews

Editorial Reviews: Review ‘Throughout the notation is carefully organized and all proofs are complete and rigorous. The text is completed by carefully worked examples, many of them are illustrated by drawings. A special feature of the book is the extensive collection of exercises … The book is a good preparation for readers who wish to go on to more advanced studies in analysis. It can be also highly recommended as a text for a course or for self study.’ Zentralblatt fur Mathematik Book Description Part one of a comprehensive text on multidimensional real analysis, including numerous exercises with partial solutions.

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

⭐(Note: As I write this I’m halfway through the first volume)Think of this two volume series as the Mother of All Multivariable Calculus books. It’s NOT an intro to multivariable calculus for someone who has finished a couple semesters of calculus; you’ll need a good stiff course (see my review of Derivatives and Integrals of Multivariable Functions by Guzman) in m.v. calculus, a dose of linear algebra, and mathematical maturity at the junior/senior undergrad level to tackle it. But if you want to go deeper – much deeper – than a first course in multivariable calculus, this is a great book.You can look inside the book and see the contents for yourself, so I’ll limit myself to general comments. The book is refreshingly free of errors (a few trivial typos are about the extent of them, at least as far as I’ve gotten) and well translated from the Dutch. There are hundreds of problems after the main text; although solutions aren’t given in general, the material is well enough explained so that the reader should be able to solve them. (one of the authors has a web site giving corrections to the text plus some solutions – see […] ).All theorems are proved in full detail, but be aware of two things: first, the proofs are “mathematicians proofs”; short and slick methods are favored over pedagogically softer ones. (example: one of the main theorems of m.v. calculus is the chain rule. Most undergrad texts would simply prove it head on from the definitions of derivative and composition of functions, but here the authors rely on a slick piece of machinery in the form of something called Hadamard’s theorem.) Second, the reader WILL have to take out her pencil and paper and fill in some details, but the good news is that the text gives enough information to make this possible in all cases.It’s a beautiful book, really – so why only 4 stars? It has to do with the old tension between the reader and writer of math texts: how explicit should the writing be? I’m dubious about the educational value of having to fill in the algebraic details, and in any case I think the text should be as explicit as possible, leaving the reader to develop his mathematical muscles in the exercises. There are a number of points where 5% more explanation by the authors would have saved the reader 50% of the effort in understanding a theorem – so I’m witholding one star as a protest. Mathematical authors beware!

⭐This is an excellent textbook – it is well written and translated to English.The author sets out to be very educational and precise and it’s a pleasure to have such rigorous definitions and proofs presented in a way that a competent aspiring mathematician would like to have them presented. All the essential explanations given without cluttering the exposition with trivialities.

⭐Este es uno de los libros de análisis multidimensional que no debe faltar en el repertorio de todo estudiante de matemáticas. Es un libro muy claro y conciso. El autor maneja con una verdadera maestría cada tema que expone relacionado con la diferenciación; partiendo de los espacios euclidianos hasta las variedades diferenciales. Lo único malo es que tiene algunos errores y detalles (nada graves) que se pueden consultar mediante un PDF que el mismo autor elaboró señalando cada página donde hay que hacer la corrección. Cabe señalar que este no es un libro para principiantes, pues para nada se trata de cálculo diferencial elemental.

⭐

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