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The Kurzweil-Henstock integral for undergraduates : a promenade along the marvelous theory of integration

  • 作者： Fonda, Alessandro, author.
  • 其他作者：
  • 其他題名：
    • Compact textbooks in mathematics.
  • 出版： Cham : Springer International Publishing :Imprint: Birkhauser
  • 叢書名： Compact textbooks in mathematics,
  • 主題： Henstock-Kurzweil integral. , Real Functions. , Measure and Integration.
  • ISBN： 9783319953212 (electronic bk.) 、 9783319953205 (paper)
  • FIND@SFXID: CGU
  • 資料類型: 電子書
  • 內容註: Functions of one real variable -- Functions of several real variables -- Differential forms -- Differential calculus in RN -- The Stokes-Cartan and the Poincare theorems -- On differentiable manifolds -- The Banach-Tarski paradox -- A brief historical note.
  • 摘要註: This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes-Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach-Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.
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  • 系統號： 005441591 | 機讀編目格式

    • 館藏資訊

    This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.

    資料來源： Google Book
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