Undergraduate analysis

Author(s)

• Lang, Serge

Bibliographic Information

Undergraduate analysis

Serge Lang

（Undergraduate texts in mathematics）

Springer, c1997

2nd ed

Note

Includes index

Description and Table of Contents

Description

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

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

by "Nielsen BookData"

Details

• NCID: BA29221275
• ISBN:
  • 0387948414
• LCCN: 96026339
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: xv, 642 p.
• Size: 24 cm
• Classification:
  • NDC9 : 413.5
  • LCC : QA300
  • DC20 : 515/.8
  • NDLC : MAA111
• Subject Headings:
  • LCSH : Mathematical analysis
• Parent Bibliography ID:
  • BA00018418