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Viser: Undergraduate Analysis

Undergraduate Analysis, 2. udgave

Undergraduate Analysis

Serge A. Lang
(2005)
Sprog: Engelsk
Springer
652,00 kr.
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Detaljer Om Varen

  • 2. Udgave
  • Hardback: 668 sider
  • Udgiver: Springer (Juni 2005)
  • ISBN: 9780387948416

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


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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