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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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  • 3.51/6 (41 bedømmelser)

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 MappingsChapter
1: Real NumbersChapter
2: Limits and Continuous FunctionsChapter
3: DifferentiationChapter
4: Elementary FunctionsChapter
5: The Elementary Real IntegralChapter
6: Normed Vector SpacesChapter
7: LimitsChapter
8: CompactnessChapter
9: SeriesChapter
10: The Integral in One VariableAppendix: The Lebesgue IntegralChapter
11: Approximation with ConvolutionsChapter
12: Fourier SeriesChapter 13, Improper IntegralsChapter
14: The Fourier IntegralChapter
15: Calculus in Vector SpacesChapter
16: The Winding Number and Global Potential FunctionsChapter
17: Derivatives in Vector SpacesChapter
18: Inverse Mapping TheoremChapter
19: Ordinary Differential EquationsChapter
20: Multiple IntegrationChapter
22: Differential FormsAppendix
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