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An illustrative introduction to modern analysis / by Nikolaos Katzourakis and Eugen Varvaruca.

By: Contributor(s): Material type: TextPublisher: Boca Raton, FL : CRC Press, an imprint of Chapman and Hall/CRC, 2018Edition: First editionDescription: 1 online resource (558 pages) : 99 illustrationsISBN:
  • 9781315195865
  • 9781351765312
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 515 23
LOC classification:
  • QA300 .K38 2018
Online resources:
Contents:
chapter 1 Sets, mappings, countability and choice / Nikos Katzourakis -- chapter 2 Metric spaces and normed spaces / Nikos Katzourakis -- chapter 3 Completeness and applications / Nikos Katzourakis -- chapter 4 Topological spaces and continuity / Nikos Katzourakis -- chapter 5 Compactness and sequential compactness / Nikos Katzourakis -- chapter 6 The Lebesgue measure on the Euclidean space / Nikos Katzourakis -- chapter 7 Measure theory on general spaces / Nikos Katzourakis -- chapter 8 The Lebesgue integration theory / Nikos Katzourakis -- chapter 9 The class of Lebesgue functional spaces / Nikos Katzourakis -- chapter 10 Inner Product Spaces and Hilbert Spaces / Nikos Katzourakis -- chapter 11 Linear operators on normed spaces / Nikos Katzourakis -- chapter 12 Weak topologies on Banach Spaces / Nikos Katzourakis -- chapter 13 Weak* topologies and compactness / Nikos Katzourakis -- chapter 14 Functional properties of the Lebesgue spaces / Nikos Katzourakis -- chapter 15 Solutions to the exercises / Nikos Katzourakis.
Abstract: Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.
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chapter 1 Sets, mappings, countability and choice / Nikos Katzourakis -- chapter 2 Metric spaces and normed spaces / Nikos Katzourakis -- chapter 3 Completeness and applications / Nikos Katzourakis -- chapter 4 Topological spaces and continuity / Nikos Katzourakis -- chapter 5 Compactness and sequential compactness / Nikos Katzourakis -- chapter 6 The Lebesgue measure on the Euclidean space / Nikos Katzourakis -- chapter 7 Measure theory on general spaces / Nikos Katzourakis -- chapter 8 The Lebesgue integration theory / Nikos Katzourakis -- chapter 9 The class of Lebesgue functional spaces / Nikos Katzourakis -- chapter 10 Inner Product Spaces and Hilbert Spaces / Nikos Katzourakis -- chapter 11 Linear operators on normed spaces / Nikos Katzourakis -- chapter 12 Weak topologies on Banach Spaces / Nikos Katzourakis -- chapter 13 Weak* topologies and compactness / Nikos Katzourakis -- chapter 14 Functional properties of the Lebesgue spaces / Nikos Katzourakis -- chapter 15 Solutions to the exercises / Nikos Katzourakis.

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.

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