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" An illustrative introduction to modern analysis "
Nikolaos Katzourakis, Eugen Vărvărucă.
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BL
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| Record Number
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562673
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b391872
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| Main Entry
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Nikos Katzourakis
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| Title & Author
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An illustrative introduction to modern analysis\ Nikolaos Katzourakis, Eugen Vărvărucă.
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| Publication Statement
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Boca Raton : CRC Press,, [2018] ©2018
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xv, 541 pages : illustrations ; 24 cm
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| ISBN
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1138718270
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: 9781138718272
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| Contents
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1 Sets, mappings, countability and choice -- 2 Metric spaces and normed spaces -- 3 Completeness and applications -- 4 Topological spaces and continuity -- 5 Compactness and sequential compactness -- 6 The Lebesgue measure on the Euclidean space -- 7 Measure theory on general spaces -- 8 The Lebesgue integration theory -- 9 The class of Lebesgue functional spaces -- 10 Inner product spaces and Hilbert spaces -- 11 Linear operators on normed spaces -- 12 Weak topologies on Banach spaces -- 13 Weak* topologies and compactness -- 14 Functional properties of the Lebesgue spaces -- 15 Solutions to the exercises.
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| Abstract
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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. With 99 graphic illustrations which complement the rigorous mathematical reasoning, this book allows the reader to develop a strong geometric intuition. Containing far beyond just theorems and rpoofs,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. With 99 graphic illustrations which complement the rigorous mathematical reasoning, this book allows the reader to develop a strong geometric intuition. Containing far beyond just theorems and rpoofs,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. With 99 graphic illustrations which complement the rigorous mathematical reasoning, this book allows the reader to develop a strong geometric intuition. Containing far beyond just theorems and rpoofs,",,,,,"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. With 99 graphic illustrations which complement the rigorous mathematical reasoning, this book allows the reader to develop a strong geometric intuition. Containing far beyond just theorems and rpoofs, it offers comments on the "know-how" and motivations for "why we do what we do". The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required, such as in Partial Differential Equations, Calculus of Variations, Harmonic Analysis, Functional Analysis, Geometric Analysis, Numerical Analysis and Applied Mathematics.
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Textbooks
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Eugen Varvaruca
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