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Undergraduate Texts in Mathematics

Undergraduate Analysis

Authors: Lang, Serge

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About this Textbook

This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises.

Reviews

Second Edition

S. Lang

Undergraduate Analysis

"[A] fine book . . . logically self-contained . . . This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."—AMERICAN MATHEMATICAL SOCIETY


Table of contents (22 chapters)

Table of contents (22 chapters)

Buy this book

eBook 49,99 €
price for Spain (gross)
  • ISBN 978-1-4757-2698-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,35 €
price for Spain (gross)
  • ISBN 978-0-387-94841-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,35 €
price for Spain (gross)
  • ISBN 978-1-4419-2853-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Undergraduate Analysis
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-2698-5
DOI
10.1007/978-1-4757-2698-5
Hardcover ISBN
978-0-387-94841-6
Softcover ISBN
978-1-4419-2853-5
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XV, 642
Number of Illustrations
23 b/w illustrations
Topics

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