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  3. A Course in Mathematical Analysis
  • Cited by 1
      • Volume 3: Complex Analysis, Measure and Integration
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2014
      May 2014
      ISBN:
      9781139424516
      9781107032040
      9781107663305
      DOI:
      https://doi.org/10.1017/CBO9781139424516
      Dimensions:
      (247 x 174 mm)
      Weight & Pages:
      0.73kg, 332 Pages
      Dimensions:
      (247 x 174 mm)
      Weight & Pages:
      0.61kg, 329 Pages
      • Subjects:
      Mathematics, Real and Complex Analysis, Geometry and Topology
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    • Selected: Digital
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    Subjects:
    Mathematics, Real and Complex Analysis, Geometry and Topology
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    Book description

    The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The Radon–Nikodym theorem is proved, and the differentiation of measures discussed.

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