Ebook Calculus on Normed Vector Spaces (Universitext)

Ebook Calculus on Normed Vector Spaces (Universitext)

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Calculus on Normed Vector Spaces (Universitext)

Ebook Calculus on Normed Vector Spaces (Universitext)

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Review

From the reviews:“Coleman (Laboratoire Jean Kuntzmann, France) generalizes the standard theorems of this subject to an arbitrary, hence possibly infinite, dimensional normed vector space, including the special cases of Banach spaces and Hilbert spaces. … Best suited for advanced undergraduate or graduate students, the text delivers the level of rigor and mathematical sophistication that one in the discipline expects from a volume published by Springer. Summing Up: Recommended. Upper-division undergraduates, graduate students, and researchers/faculty.” (D. S. Larson, Choice, Vol. 50 (10), June, 2013)“It covers all topics of classical calculus in the broad setting of real normed spaces. … The style used in giving a complete overview of all these topics of differential calculus is a really nice one, introducing concepts whenever they are needed … . Each chapter contains a variety of interesting exercises which help to complement the material being studied. Therefore, to finish, I highly recommend this book to teachers and researchers on the subject.” (Jesús Ferrer, Mathematical Reviews, March, 2013)

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From the Back Cover

This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

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Product details

Series: Universitext

Paperback: 264 pages

Publisher: Springer; 2012 edition (July 24, 2012)

Language: English

ISBN-10: 9781461438939

ISBN-13: 978-1461438939

ASIN: 1461438934

Product Dimensions:

6.1 x 0.6 x 9.2 inches

Shipping Weight: 13.6 ounces (View shipping rates and policies)

Average Customer Review:

4.0 out of 5 stars

1 customer review

Amazon Best Sellers Rank:

#3,248,035 in Books (See Top 100 in Books)

This is a more approachable presentation of what Henri Cartan does in his "Differential Calculus", originally in French and now out of print, at least in the English translation. Usually an undergraduate mathematics student takes a multivariable calculus course and then, either as an undergraduate or graduate student, learns smooth manifolds modelled on n-dimensional Euclidean space. This amounts to dropping the hypothesis of the space being linear (at each point the tangent space is linear, but the space itself is now not demanded to be a linear space), but keeping the condition of working with n-dimensional Euclidean space. In fact I think it is useful between a multivariable calculus course and a smooth manifolds course to learn what is done in this book and Cartan, calculus done in a way that works with any normed space rather than finite dimensional linear spaces. Things that are identified when working in n-dimensional Euclidean space are thus seen to be objects that are related but not identical, like the gradient and the derivative. This is also the right language to understand the Hessian. Things like the Fréchet derivative and the Gâteaux derivative are not esoteric and should feel natural to work with, and they are a systematic way of doing the calculus of variations. Coleman has chapters on flows of vector fields, a hugely useful topic, and a chapter on the calculus of variations done using differential calculus in Banach spaces.

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