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The Resource From classical to modern analysis, Rinaldo B. Schinazi

From classical to modern analysis, Rinaldo B. Schinazi

Label
From classical to modern analysis
Title
From classical to modern analysis
Statement of responsibility
Rinaldo B. Schinazi
Creator
Author
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Schinazi, Rinaldo B.
Dewey number
515
Illustrations
illustrations
Index
index present
LC call number
QA300
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
Mathematical analysis
Label
From classical to modern analysis, Rinaldo B. Schinazi
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
1 online resource (xii, 270 pages)
File format
unknown
Form of item
online
Isbn
9783319945828
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-94583-5
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Label
From classical to modern analysis, Rinaldo B. Schinazi
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
1 online resource (xii, 270 pages)
File format
unknown
Form of item
online
Isbn
9783319945828
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-94583-5
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote

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