From Classical to Modern Analysis. 1st ed. 2018

種類:

電子ブック

責任表示:

by Rinaldo B. Schinazi

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Schinazi, Rinaldo B.
• SpringerLink (Online service)

ISBN:

9783319945835 [3319945831]    

注記:

Preface -- Real Numbers -- Sequences of Real Numbers -- Limits Superior and Inferior of a Sequence -- Numerical Series -- Convergence of Functions -- Power Series -- Metric Spaces -- Topology in a Metric Space -- Continuity on Metric Spaces -- Measurable Sets and Measurable Functions -- Measures -- The Lebesgue Integral -- Integrals with Respect to Counting Measures -- Riemann and Lebesgue Integrals -- Modes of Convergance -- References.
This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis. To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The l

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