Undergraduate Analysis

Undergraduate Analysis by Serge Lang.

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...

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Bibliographic Details
Main Author: Lang, Serge (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1997.
Edition:2nd ed. 1997.
Series:Undergraduate Texts in Mathematics,
Springer eBook Collection.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • One Review of Calculus
  • 0 Sets and Mappings
  • I Real Numbers
  • II Limits and Continuous Functions
  • III Differentiation
  • IV Elementary Functions
  • V The Elementary Real Integral
  • Two Convergence
  • VI Normed Vector Spaces
  • VII Limits
  • VIII Compactness
  • IX Series
  • X The Integral in One Variable
  • Three Applications of the Integral
  • XI Approximation with Convolutions
  • XII Fourier Series
  • XIII Improper Integrals
  • XIV The Fourier Integral
  • Four Calculus in Vector Spaces
  • XV Functions on n-Space
  • XVI The Winding Number and Global Potential Functions
  • XVII Derivatives in Vector Spaces
  • XVIII Inverse Mapping Theorem
  • XIX Ordinary Differential Equations
  • Five Multiple Integration
  • XX Multiple Integrals
  • XXI Differential Forms.

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