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From classical to modern analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	From classical to modern analysis/ by Rinaldo B. Schinazi.
作者:	Schinazi, Rinaldo B.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xii, 270 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Mathematical analysis. -
電子資源:	https://doi.org/10.1007/978-3-319-94583-5
ISBN:	9783319945835

From classical to modern analysis
Schinazi, Rinaldo B.

From classical to modern analysis[electronic resource] /by Rinaldo B. Schinazi. - Cham :Springer International Publishing :2018. - xii, 270 p. :ill., digital ;24 cm.

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 last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

ISBN: 9783319945835

Standard No.: 10.1007/978-3-319-94583-5doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA300 / .S356 2018

Dewey Class. No.: 515

From classical to modern analysis
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520 $a 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 last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.
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