Katzourakis / Varvaruca An Illustrative Introduction to Modern Analysis

1. Auflage 2017
ISBN: 978-1-351-76533-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 558 Seiten

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.

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.

Autoren/Hrsg.

Katzourakis, Nikolaos

Varvaruca, Eugen

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Some basics from Calculus and Set Theory. Metric spaces. Topological Spaces. Completeness. Compactness. Inner Product Spaces and Hilbert Spaces. Linear Operators on Banach Spaces. Weak Topologies on Banach spaces. Weak* Topologies and weak compactness. The Lebesgue measure on the Euclidean space. Measures and Integration on general spaces. Basic Theory of Lebesgue spaces. Exercises and Solutions.

Über Autor(innen)

Nikos Katzourakis is based at the University of Reading in the UK. His field of expertise lies in the analysis of nonlinear Partial Differential Equations and Calculus of Variations. His name is connected to contributions in vectorial variational problems for supremal functionals and generalised solutions for fully nonlinear systems.

Eugen Varvaruca is based at the University "Al. I. Cuza’’ of Iasi in Romania. His research work is concerned with the analysis of nonlinear Partial Differential Equations, focusing particularly on free-boundary problems in fluid dynamics. In 2012 he was awarded the Whitehead Prize by the London Mathematical Society for his contributions.