Authors:
- Presents an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level
- One of the few textbooks to bridge the gap between the available elementary texts and high level texts
- Includes many non-trivial applications of the theory and interesting exercises
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)Authors and Affiliations
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Campus de Saint-Martin-d’Héres, Laboratoire Jean Kuntzmann, Grenoble, France
Rodney Coleman
About the author
Bibliographic Information
Book Title: Calculus on Normed Vector Spaces
Authors: Rodney Coleman
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-3894-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2012
Softcover ISBN: 978-1-4614-3893-9Published: 24 July 2012
eBook ISBN: 978-1-4614-3894-6Published: 25 July 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XI, 249
Topics: Functional Analysis, Optimization