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Undergraduate analysis / Serge Lang

Main Author Lang, Serge, 1927-2005 Country Estados Unidos. Edition 2nd ed Publication New York : Springer, cop. 1997 Description XV, 642 p. : il. ; 25 cm Series Undergraduate texts in mathematics ISBN 0-387-94841-4 CDU 517
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Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca da UMinho no Campus de Azurém
BPG2 517 - L Available 205457
Monografia Biblioteca da UMinho no Campus de Azurém
BPG 517 - L Available 335393
Monografia Biblioteca da UMinho no Campus de Azurém
BPG2 517 - L Available 423955
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Enhanced descriptions from Syndetics:

This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.

From the reviews: "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 provided by Syndetics

  • Chapter 0 Sets and Mappings
  • Chapter 1 Real Numbers
  • Chapter 2 Limits and Continuous Functions
  • Chapter 3 Differentiation
  • Chapter 4 Elementary Functions
  • Chapter 5 The Elementary Real Integral
  • Chapter 6 Normed Vector Spaces
  • Chapter 7 Limits
  • Chapter 8 Compactness
  • Chapter 9 Series
  • Chapter 10 The Integral in One Variable
  • Appendix: The Lebesgue Integral
  • Chapter 11 Approximation with Convolutions
  • Chapter 12 Fourier Series
  • Chapter 13 Improper Integrals
  • Chapter 14 The Fourier Integral
  • Chapter 15 Calculus in Vector Spaces
  • Chapter 16 The Winding Number and Global Potential Functions
  • Chapter 17 Derivatives in Vector Spaces
  • Chapter 18 Inverse Mapping Theorem
  • Chapter 19 Ordinary Differential Equations
  • Chapter 20 Multiple Integration
  • Chapter 22 Differential Forms
  • Appendix

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