Overview
- Starts from basic concepts and extends to n-dimensional, multi-variable real analysis
- Self-contained, with easy-to-follow proofs
- Provides elegant proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem
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About this book
This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry.
With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
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Keywords
Table of contents (10 chapters)
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Front Matter
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One Variable Real Analysis
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Front Matter
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Multi-Variable Advanced Calculus
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Front Matter
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Back Matter
Authors and Affiliations
About the author
Fabio Botelho holds a PhD in Mathematics from Virginia Tech, USA, and a Master in Aeronautics and Mechanics Engineering from the Aeronautics Institute of Technology, Brazil. He is the author of the book "Functional Analysis and Applied Optimization in Banach Spaces," also published with Springer. His main research fields are calculus of variations, convex analysis and duality applied to problems in physics and engineering.
Bibliographic Information
Book Title: Real Analysis and Applications
Authors: Fabio Silva Botelho
DOI: https://doi.org/10.1007/978-3-319-78631-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-78630-8Published: 24 May 2018
Softcover ISBN: 978-3-030-08750-0Published: 26 December 2018
eBook ISBN: 978-3-319-78631-5Published: 14 May 2018
Edition Number: 1
Number of Pages: XIII, 567
Topics: Real Functions, Measure and Integration, Sequences, Series, Summability